Solution theory for the stochastic thin film equation with spatially colored noise

We review recent results on the weak and strong solution theory for the stochastic thin-film equation driven by Gaussian noise, which is white in time and colored in space. In particular, we discuss the effect of intermolecular van der Waals forces between the fluid and the substrate in more detail. We demonstrate that they result in a strictly positive and smooth film height which persists for all times. We also touch upon open questions and possible extensions of the presented results. The talk is based on joint work with Antonio Agresti, Konstaninos Dareiotis, Benjamin Gess and Manuel Gnann.