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Title:
Hamiltonian dynamics of fluids and vortex sheets
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Abstract:
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. This framework, in particular, allows one to define symplectic structures on the spaces of vortex sheets.
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