Geometric and variational features of the Euler equations

Yann Brenier, CNRS, Université de Nice, FR Wolfgang Döblin

Following V.I. Arnold, we know that the motion of an inviscid incompressible fluid moving in a domain D follows a geodesic curve along the group of volume preserving diffeomorphisms for the metric induced by L². We show how the concept of generalized flows can help to understand the geometry of this group.