Local-existence for the Inhomogeneous Muskat problem

Abstract

In this work we study the evolution of the interface between two different fluids in a porous media with two different permeabilities. We prove local existence in Sobolev spaces, when the free boundary is given by the discontinuity among the densities and viscosities of the fluids.

References in corpus (1)

• On the Muskat problem: global in time results in 2D and 3D

Cited by in corpus (4)

• A paradifferential approach for well-posedness of the Muskat problem
• Global existence and decay of the inhomogeneous Muskat problem with Lipschitz initial data
• Global Results for the Inhomogeneous Muskat Problem
• On the dynamics of thin layers of viscous flows inside another viscous fluid