Workshop: Geometry of singular vorticities in the Euler hydrodynamics, Boris Khesin

Date: 2023-09-11

Time: 14:00 - 14:50

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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 binormal equation in higher-dimensions and its explicit solutions that collapse in finite time. On the other hand, by going to lower dimensions, we observe a curious appearance of the golden ratio in the motion of point vortices in the plane. We also describe a puzzle relating Hamiltonian approximations and seeming attractors in 2D ideal hydrodynamics.