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Relaxation of the incompressible porous media equation

László Székelyhidi Jr (2012)

Annales scientifiques de l'École Normale Supérieure

It was shown recently by Córdoba, Faraco and Gancedo in [1] that the 2D porous media equation admits weak solutions with compact support in time. The proof, based on the convex integration framework developed for the incompressible Euler equations in [4], uses ideas from the theory of laminates, in particular T 4 configurations. In this note we calculate the explicit relaxation of IPM, thus avoiding T 4 configurations. We then use this to construct weak solutions to the unstable interface problem (the...

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