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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

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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