To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract:

Large scale dynamics of the oceans and the atmosphere are commonly governed by the primitive equations (PEs), also known as Hydrostatic Euler Equations. While it is by now well-known that the 3D viscous primitive equations are globally well-posed in Sobolev spaces, my talk will solely focus on the invisicd case. First, I will briefly discuss the ill posedness in Sobolev spaces, the local well-posedness in the space of analytic functions, and finite-time blowup of solution to the 3D inviscid PEs with rotation (Coriolis force). Then I will also show, in the case of “well-prepared” analytic initial data, the regularizing effect of the Coriolis force by providing a lower bound for the life-span of the solutions that grows toward infinity with the rotation rate. These are joint works with T. E. Ghoul, Q. Lin and E. S. Titi.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract:

In this talk, we will discuss the regularity theory and long-time behavior of solutions to the Euler Alignment model, focusing on the properties of the limiting density profile, which is in general a measure.  We show that for unidirectional data, the geometric structure of the singular support of this measure, i.e., the "mass concentration" set, can be understood almost completely in terms of the initial data.  

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

Let X be a smooth complex projective variety with homogeneous ideal I. We consider the question of bounding the saturation degree of the powers I^a of I, ie the degrees
after which this power agrees with the symbolic power I^(a). I’ll discuss joint work with Lawrence Ein and Tai Huy Ha giving results in two situations:
—    When I is the ideal of a smooth curve C, we give a bound in terms of the regularity of C, extending results of Geramita et al, Sidman, Chandler and others in the case of finite sets;
—    When X is smooth of arbitrary dimension, we give a bound in terms of the degrees of defining equations that has the same general shape as (but a rather different proof
than) regularity bounds established many years ago with Bertram and Ein.

I will also discuss a number of open questions.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract: 

Convection is buoyancy-driven flow resulting from unstable density stratification in the presence of a gravitational field.  Beyond its central role in myriad engineering heat transfer applications, convection underlies many of nature’s dynamical designs on larger-than-human scales. Indeed, solar heating of Earth’s surface generates buoyancy forces that cause the winds to blow, which in turn drive the oceans’ flow.  Convection in Earth’s mantle on geological timescales makes the continents drift, and thermal and compositional density differences induce buoyancy forces that drive a dynamo in Earth’s liquid metal core—the dynamo that generates the magnetic field protecting us from solar wind that would otherwise extinguish life as we know it on the surface.  The structure of the Sun itself relies on convection in the outer layers to transfer heat from the interior to radiate away from the surface.

The key feature of convection is transport: thermal convection actively transports the heat that generates the density variations that produce the buoyancy forces.  Determining the rate at which “heat rises” in turbulent convection is one of the most important open problems in fluid dynamics.  In this presentation the confounding question of asymptotically high Rayleigh number heat transport in Rayleigh-Bénard convection – the buoyancy-driven flow in a horizontal layer of fluid heated from below modeled by the Boussinesq approximation to the Navier-Stokes equations – is reviewed from viewpoints of theory (models of the model), computation (direct numerical simulations), experiment (laboratory tests), and mathematical analysis (theorems).

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

Abstract: The log canonical threshold is an invariant that measures how singular a hypersurface over an algebraically closed field of characteristic zero is. The F-pure threshold is the positive characteristic analog. Hypersurfaces with smaller threshold are more singular.
I will discuss a lower bound for a homogeneous polynomial in characteristic p, relative to its degree, and describe the classification of the hypersurfaces that achieve this bound up to change of coordinates. These results were obtained as part of a project started at the A.W.M. Workshop ``Women in Commutative Algebra” at B.I.R.S.; joint work with Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page, Jyoti Singh, Karen E. Smith and Emily Witt.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

Let R_n be the polynomial ring with n variables over a field K. We consider the natural action of the n-th symmetric group S_n to R_n. In this talk, I will mainly talk about the following problem: Fix monomials u_1,\dots,u_m and consider the ideal I_n of R_n generated by the S_n-orbits of these monomials. How the Betti numbers of I_n change when n increases?
I will explain that there is a simple way to determine non-zero positions of the Betti table of I_n when n is sufficiently large. I also explain that we can determine the Betti numbers of I_n by considering the S_n-module structure of Tor_i(I_n,K).
The above problem is motivated by recent studies of algebraic properties of S_n-invariant ideals and is inspired by studies of Noetherianity up to symmetry. I will explain this motivation and basic combinatorial properties of S_n-invariant ideals in the first part of the talk.
This talk includes a joint work with Claudiu Raicu.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Abstract:

I will consider the 2D incompressible Euler equation in a simply-connected bounded domain. Such domains admit stationary points with the following property: a single point vortex located at that position will not move. In this talk I will discuss the problem of the long time confinement of the vorticity around such a stationary point. This is joint work with Martin Donati.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To attend this seminar, you must register in advance, by clicking HERE.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

Tea for members and participants.

To participate, please register here: https://www.msri.org/seminars/25657

To participate in this seminar, please register here: https://www.msri.org/seminars/25657

A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no prerequisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25657