Abstract:
We describe a striking connection between Arnold's least-action principle for
incompressible Euler flows and geodesic paths for Wasserstein distance.
The least-action problem for geodesic distance on the `manifold'
of fluid-blob shapes exhibits instability due to microdroplet formation.
A connection with fluid mixture models via a variant of Brenier's relaxed
least-action principle for generalized Euler flows will be outlined also.
This is joint work with Bob Pego and Dejan Slepcev. |