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Lie groupoids and vortex sheets

Banff International Research Station for Mathematical Innovation and Discovery

In 1966, V.Arnold suggested a group-theoretic framework for ideal hydrodynamics. In this approach, the motion of an incompressible fluid on a Riemannian manifold is described as the geodesic flow of a right-invariant metric on the group of volume-preserving diffeomorphisms. In my talk, I will review Arnold's picture and show how it can be extended to incorporate certain discontionus fluid motions, known as vortex sheets. This is done by replacing groups and algebras in Arnold's approach by certain groupoids and algebroids. This is joint work with B.Khesin.

Mathematics; Dynamical systems and ergodic theory; Ordinary differential equations; Dynamical systems

video/mp4

Author affiliation: University of Toronto

2017-01-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60026

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/