On a thin film model with insoluble surfactant

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