Non-negative global weak solutions for a degenerate parabolic system modeling thin films driven by capillarity

TL;DR

This paper proves the global existence of nonnegative weak solutions for a complex degenerate parabolic system modeling the behavior of two thin fluid layers driven solely by capillarity in a porous medium.

Contribution

It establishes the existence of solutions for a coupled, fourth-order degenerate system, advancing understanding of thin film dynamics driven by capillarity.

Findings

Global existence of nonnegative weak solutions proven

Applicable to systems modeling thin fluid layers in porous media

Addresses degenerate, fourth-order parabolic equations

Abstract

We prove global existence of nonnegative weak solutions for a strongly coupled, fourth order degenerate parabolic system governing the motion of two thin fluid layers in a porous medium when capillarity is the sole driving mechanism.