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The Hasimoto transform, skew-mean-curvature flow, and Euler singularity problem

Mathematical Physics and Probability Seminar

The Hasimoto transform, skew-mean-curvature flow, and Euler singularity problem
Series: Mathematical Physics and Probability Seminar
Location: MATH 402
Presenter: Boris Khesin, University of Toronto

The binormal (or vortex filament) equation provides the localized induction approximation of the 3D incompressible Euler equation. We present a Hamiltonian framework for the the binormal equation in higher-dimensions and its explicit solutions that collapse in finite time. The local nature of this phenomenon may suggest the appearance of singularity in nearby vortex blob solutions of the Euler equation in 5D and higher.