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Fluids, vortex sheets, and skew-mean-curvature flows

Fluid Mechanics, Hamiltonian Dynamics, and Numerical Aspects of Optimal Transportation October 14, 2013 - October 18, 2013

October 18, 2013 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Boris Khesin (University of Toronto)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC


Abstract We show that an approximation of the hydrodynamical Euler equation describes the skew-mean-curvature flow on vortex membranes in any dimension. This generalizes the classical binormal, or vortex filament, equation in 3D. We present a Hamiltonian framework for higher-dimensional vortex filaments and vortex sheets as singular 2-forms with support of codimensions 2 and 1, respectively. This framework, in particular, allows one to define symplectic structures on the spaces of vortex sheets.
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