Mixing solutions for the Muskat problem

2016/05/16 by Castro, Ángel, Córdoba, Diego, Faraco, Daniel · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.04822

Abstract

We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type H⁵ 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.

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