PDE Real Analysis Seminar

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Date, time & place Tuesday 10:30 - 11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

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2018/10/23

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Jian-Guo Liu (Duke University)
Least action principle for incompressible flow with free boundary (English)
[ Abstract ]
In this talk I will describe a connection between Arnold's least-action principle for incompressible flows with free boundary 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. Using a conformal map formulation we investigate singularity formation in water-wave dynamics neglecting gravity. A connection with fluid mixture models via a variant of Brenier's relaxed least-action principle for generalized Euler flows will also be discussed.