Hamiltonian dynamics of fluids and vortex sheets.

  • Boris Khesin (University of Toronto, Department of Mathematics, USA)
A3 01 (Sophus-Lie room)


We show that an approximation of the hydrodynamical Euler equation describes the binormal 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.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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