Nonlinear Waves Trimester - June Conference

Collection Nonlinear Waves Trimester - June Conference

Organizer(s) T. Duyckaerts, F. Merle, J. Szeftel

Date(s) 20/06/2016 - 24/06/2016

linked URL https://indico.math.cnrs.fr/event/892/overview

00:00:00 / 00:00:00

18 23

On global regularity for the 2D Muskat equations with finite slope

Also appears in collection : ECM 2024 Plenary Speakers

We consider the 2D Muskat equation for the interface between two constant density fluids in an incompressible porous medium, with velocity given by Darcy's law. We establish that as long as the slope of the interface between the two fluids remains bounded and uniformly continuous, the solution remains regular. The proofs exploit the nonlocal nonlinear parabolic nature of the equations through a series of nonlinear lower bounds for nonlocal operators. These are used to deduce that as long as the slope of the interface remains uniformly bounded, the curvature remains bounded. We provide furthermore a global regularity result for small initial data: if the initial slope of the interface is sufficiently small, there exists a unique solution for all time. This is joint work with P. Constantin, F. Gancedo, and R. Shvydkoy.

Information about the video

Date of recording 23/06/2016
Date of publication 04/07/2016
Institution IHES
Format MP4

Domain(s)

Analysis of PDEs

MSC codes

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