We consider the evolution of two incompressible, immiscible fluids with different densities in porous media, known as the Muskat problem , which in two dimensions is analogous to the Hele-Shaw cell . We establish, for a class of large and monotone initial data, the global existence of weak solutions. The proof is based on a local well-posedness result for the initial data with certain specific asymptotics at spatial infinity and a new maximum principle for the first derivative of the graph function.
ASJC Scopus subject areas
- Applied Mathematics