Piecewise constant subsolutions for the Muskat problem (Q1795130)

The authors target the existence of infinitely many admissible weak solutions for the incompressible porous media equations for all Muskat-type initial data with \(C^{3,\alpha}\)-regularity of the interface in the unstable regime as well as for all non-horizontal data with \(C^{3,\alpha}\)-regularity in the stable regime. The key idea of the working methodology is to construct admissible subsolutions with piecewise constant densities.