Geodesic Framework for Vortex Sheets and Generalized Fluid Flows

Explore the geodesic framework for vortex sheets and generalized fluid flows in this comprehensive lecture from the Workshop on Geometry and Analysis of Fluid Flows. Delve into Boris Khesin's discussion on the implications of Arnold's group-theoretic approach to ideal hydrodynamics, viewed as a geodesic flow for a right-invariant metric on the group of volume-preserving diffeomorphisms. Discover how equations in mathematical physics, including vortex sheet motion and fluids with moving boundaries, exhibit Lie groupoid symmetries rather than Lie group symmetries. Examine the geodesic setting for these phenomena, which extends to describing multiphase fluids, homogenized vortex sheets, and Brenier's generalized flows. Gain insights from this joint work with Anton Izosimov, presented at the University of Toronto as part of a special tribute to David Ebin.