On the Muskat problem with data in critical Sobolev spaces.

Abstract: The Muskat problem is a nonlinear and nonlocal equation that models the dynamics of the interface of two incompressible and immiscible fluids separated by a porous media. I will present a recent global well-posedness result in critical Sobolev spaces for the 3D Muskat problem that allows the 2D interface to be arbitrarily large in the Lipschitz semi-norm (joint with F. Gancedo).

analysis of PDEs

Audience: researchers in the topic

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PDE seminar via Zoom