Mixing solutions for the Muskat problem

By A. Castro, D. C'ordoba, Daniel Faraco. Inventiones Mathematicae, 2016

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We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type H5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^5$$\end{document} 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

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