Porous media: The Muskat problem in three dimensions
Antonio Córdoba, Diego Córdoba, Francisco Gancedo · Analysis & PDE · 2013
The Muskat problem involves filtration of two incompressible fluids through a porous medium.We consider the problem in three dimensions, discussing the relevance of the Rayleigh-Taylor condition and the topology of the initial interface, in order to prove the local existence of solutions in Sobolev spaces.