On a thin film model with insoluble surfactant

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 medium sized initial data in large function spaces. Moreover, exponential decay towards the flat equilibrium state is established, where an estimate on the decay rate can be computed explicitly