Global Results for the Inhomogeneous Muskat Problem

Abstract

The inhomogeneous Muskat problem models the dynamics of an interface between two fluids of differing characteristics inside a non-uniform porous medium. We consider the case of a porous media with a permeability jump across a horizontal boundary away from an interface between two fluids of different viscosities and densities. For initial data of explicit medium size, depending on the characteristics of the fluids and porous media, we will prove the global existence and uniqueness of a solution which is instantly analytic and decays in time to the flat interface.

References in corpus (7)

• On the global existence for the Muskat problem
• On The Muskat Problem With Viscosity Jump: Global In Time Results
• Global wellposedness for the 3D Muskat problem with medium size slope
• Global well-posedness for the three dimensional Muskat problem in the critical Sobolev space
• Local-existence for the Inhomogeneous Muskat problem
• Global solutions for the Muskat problem in the scaling invariant Besov space ${\dot{B}}_{\infty ,1}^1$
• Global existence and decay of the inhomogeneous Muskat problem with Lipschitz initial data

Cited by in corpus (1)

• Global existence and decay of the inhomogeneous Muskat problem with Lipschitz initial data