Splash singularities for the one-phase Muskat problem in stable regimes

This paper shows finite time singularity formation for the Muskat problem in a stable regime. The framework we exhibit is with a dry region, where the density and the viscosity are set equal to 0 (the gradient of the pressure is equal to (0, 0)) in the complement of the fluid domain. The singularity is a splash-type: a smooth fluid boundary collapses due to two different particles evolve to collide at a single point. This is the first example of a splash singularity for a parabolic problem.Ministerio de Ciencia e InnovaciónEuropean Research CouncilNational Science FoundationOffice of Naval Researc