Variational models for incompressible Euler equations

Tuesday, February 23, 2010 - 3:30pm - 4:15pm
EE/CS 3-180
Alessio Figalli (The University of Texas at Austin)
Keywords: Incompressible Euler equations, Arnold
distance, Relaxation

Abstract: According to Arnold's interpretation, the Euler equations for
incompressible fluids can be seen as a geodesic equation in the space of
measure preserving diffeomorphism. Hence, one can look for solutions by
minimizing the geodesic action functional with fixed endpoints. Since this
problem is in general ill-posed, Brenier introduced at the end of the 80's
a relaxed version of Arnold's approach. The aim of the talk is to describe
some recent results on this problem.
MSC Code: