Non-negative global weak solutions for a degenerated parabolic system approximating the two-phase Stokes problem

TL;DR

This paper proves the existence of non-negative global weak solutions for a degenerated parabolic system modeling two-phase flows influenced by capillary forces, extending classical thin film equations.

Contribution

It introduces a new existence result for a coupled degenerated system as an approximation of the two-phase Stokes problem.

Findings

Existence of non-negative global weak solutions established.

The system generalizes the classical Thin Film equation to two-phase flows.

Provides mathematical foundation for modeling two-phase capillary-driven flows.

Abstract

We establish the existence of non-negative global weak solutions for a strongly couple degenerated parabolic system which was obtained as an approximation of the two-phase Stokes problem driven solely by capillary forces. Moreover, the system under consideration may be viewed as a two-phase generalization of the classical Thin Film equation.