Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773455 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2017 | 33 Pages |
Abstract
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. The nonlinear bounds then allow us to obtain local existence for arbitrarily large initial data in the class W2,p, 1
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Peter Constantin, Francisco Gancedo, Roman Shvydkoy, Vlad Vicol,