Title: Fluids, vortex membranes, and skew-mean-curvature flows

Abstract:

The classical binormal equation is an integrable Hamiltonian system describing an evolution of a curve in 3D. It is known to be equivalent to many other systems, including the vortex filament equation, the NLS equation, a 1D compressible fluid, and a version of the Landau-Lifschitz equation. In the talk we describe an analog of the binormal equation in any dimension. It turns out that an approximation of the hydrodynamical Euler equation describes the skew-mean-curvature flow on vortex membranes of codimension 2 in R^n. We present a Hamiltonian framework for dynamics of higher-dimensional vortex filaments and vortex sheets as singular 2-forms (Green currents) with support of codimensions 2 and 1, respectively.

Wednesday, Feb. 17, 4:30 – 5:30 p.m.
Mathematics 520
Tea will be served at 4:00 p.m.

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