Relaxation of the incompressible porous media equation
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 configurations. In this note we calculate the explicit relaxation of IPM, thus avoiding configurations. We then use this to construct weak solutions to the unstable interface problem (the...