Mixing solutions for the Muskat problem
Abstract
We prove the existence of mixing solutions of the incompressible porous media equation for all Muskat type $H^5$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2016
- DOI:
- 10.48550/arXiv.1605.04822
- arXiv:
- arXiv:1605.04822
- Bibcode:
- 2016arXiv160504822C
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- 73 pages, 2 figures. This version includes the case of variable opening of the mixing zone and emphasizes the semiclassical analysis viewpoint