# On a thin film model with insoluble surfactant

## TL;DR

This paper investigates the mathematical properties of a thin film model with insoluble surfactant, proving the existence of solutions and their exponential decay to equilibrium under various physical forces.

## Contribution

It establishes the existence of global weak solutions for medium initial data and provides explicit decay rates towards equilibrium in a complex physical setting.

## Key findings

- Existence of global weak solutions for medium initial data.
- Exponential decay towards flat equilibrium state.
- Explicit decay rate estimates provided.

## Abstract

This paper studies the existence and asymptotic behavior of global weak solutions for a thin film equation with insoluble surfactant under the influence of gravitational, capillary and van der Waals forces. We prove the existence of global weak solutions for \emph{medium sized} initial data in \emph{large function spaces}. Moreover, exponential decay towards the flat equilibrium state is established, where an estimate on the decay rate can be computed explicitly.