Martingale solutions to the stochastic thin-film equation in two dimensions
- Authors: Max Sauerbrey
- Preprint year: 2021
- First public date: 2021-08-12
- arXiv: 2108.05754
- Status: Published
- Publication type: Journal article
- Publication year: 2024
- Journal: Annales de l’Institut Henri Poincaré B 60(1), 373–412 (2024)
- DOI: 10.1214/22-AIHP1328
Abstract
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.