Mixing solutions for the Muskat problem
Analysis of PDEs
2021-03-15 v2
Abstract
We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type initial data in the fully unstable regime. The proof combines convex integration, contour dynamics and a basic calculus for non smooth semiclassical type pseudodifferential operators which is developed.
Cite
@article{arxiv.1605.04822,
title = {Mixing solutions for the Muskat problem},
author = {Ángel Castro and Diego Córdoba and Daniel Faraco},
journal= {arXiv preprint arXiv:1605.04822},
year = {2021}
}
Comments
73 pages, 2 figures. This version includes the case of variable opening of the mixing zone and emphasizes the semiclassical analysis viewpoint