Existence and stability of weak solutions for a degenerate parabolic system modelling two-phase flows in porous media

TL;DR

This paper proves the global existence and exponential stability of weak solutions for a degenerate parabolic system modeling two-phase flows in porous media, advancing understanding of such complex fluid interactions.

Contribution

It establishes the existence and stability of weak solutions for a degenerate parabolic system modeling two-phase flows, which was previously unproven.

Findings

Global existence of nonnegative weak solutions

Exponential convergence to flat equilibria

Modeling of two-phase fluid interactions in porous media

Abstract

We prove global existence of nonnegative weak solutions to a degenerate parabolic system which models the interaction of two thin fluid films in a porous medium. Furthermore, we show that these weak solutions converge at an exponential rate towards flat equilibria.