$L^2$-geometry of diffeomorphism groups and the equations of hydrodynamics

PDE Seminar
Tuesday, January 28, 2014 - 3:00pm
1 hour (actually 50 minutes)
Skiles 006
University of Notre Dame
In 1966 V. Arnold observed that solutions to the Euler equations of incompressible fluids can be viewed as geodesics of the kinetic energy metric on the group of volume-preserving diffeomorphisms. This introduced Riemannian geometric methods into the study of ideal fluids. I will first review this approach and then describe results on the structure of singularities of the associated exponential map and (time premitting) related recent developments.