DMS Colloquium: Jian-Guo Liu

Speaker: Jian-Guo Liu, Duke University

Title: Microdroplet Instability in a Least-Action Principle for Incompressible Fluids

Abstract: In this talk, I will 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 micro-droplet formation. We will show that the Wasserstein geodesic is given by a weak solution to a compressible pressure-less equation and it is a limit of a sequence of weak solutions to incompressible Euler equation. A connection with fluid mixture models via a variant of Brenier’s relaxed least action principle for generalized Euler flows will be outlined.

This is a joint work with Bob Pego, and Dejan Slepcev.

Host: Wenxian Shen