Abstract for the talk at 22.07.2014 (16:45 h)Oberseminar ANALYSIS - PROBABILITY
Boris Khesin (University of Toronto, Department of Mathematics, USA)
Hamiltonian dynamics of fluids and vortex sheets.
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.