Martingale solutions to the stochastic thin-film equation in two dimensions

We construct solutions to the stochastic thin-film equation with quadratic mobility and Stratonovich gradient noise in the physically relevant dimension d = 2 and allow in particular for solutions with non -full support. The construction relies on a Trotter- Kato time -splitting scheme, which was recently employed in d = 1. The additional analytical challenges due to the higher spatial dimension are overcome using alpha-entropy estimates and corresponding tightness arguments.