Weak solutions to a thin film model with capillary effects and insoluble surfactant

TL;DR

This paper proves the existence of nonnegative weak solutions for a complex thin film model involving insoluble surfactant and capillary effects, advancing mathematical understanding of such physical phenomena.

Contribution

It establishes the existence of weak solutions for a coupled degenerate parabolic system modeling thin film and surfactant dynamics, under natural assumptions.

Findings

Existence of nonnegative weak solutions proven.

Coupled degenerate parabolic system analyzed.

Model includes capillary effects and insoluble surfactant.

Abstract

The paper focuses on a model describing the spreading of an insoluble surfactant on a thin viscous film with capillary effects taken into account. The governing equation for the film height is degenerate parabolic of fourth order and coupled to a second order parabolic equation for the surfactant concentration. It is shown that nonnegative weak solutions exist under natural assumptions on the surface tension coefficient.