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Analysis Seminar

Thursday, March 29, 2018 - 12:00pm

Jian-Guo Liu

Duke University


University of Pennsylvania


Please note the special time and the special room.

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 presure-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. 

I will discuss a conformal mapping formulation for two-dimensional water wave equations. I will discuss  a pseudo-spectral numerical schemes in this formulation and present spectral error analysis. 

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