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TOD

Seminar

The filament equation in any dimension

Khesin, B (University of Toronto)
Wednesday 25 July 2012, 09:00-09:40

Seminar Room 1, Newton Institute

Abstract

We show that the LIA approximation of the incompressible 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 the symplectic structures on the spaces of vortex sheets.

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