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The filament equation in any dimension
If you have a question about this talk, please contact Mustapha Amrani.
Topological Dynamics in the Physical and Biological Sciences
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.
This talk is part of the Isaac Newton Institute Seminar Series series.
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