The stochastic thin-film equation: existence of nonnegative martingale solutions
- Authors: Benjamin Gess, Manuel V. Gnann
- Preprint year: 2019
- First public date: 2019-04-18
- arXiv: 1904.08951
- Status: Published
- Publication type: Journal article
- Publication year: 2020
- Journal: Stochastic processes and their applications, 130 (2020) 12, pp. 7260-7302
- DOI: 10.1016/j.spa.2020.07.013
Abstract
We consider the stochastic thin-film equation with colored Gaussian Stratonovich noise in one space dimension and establish the existence of nonnegative weak (martingale) solutions. The construction is based on a Trotter-Kato-type decomposition into a deterministic and a stochastic evolution, which yields an easy to implement numerical algorithm. Compared to previous work, no interface potential has to be included, the initial data and the solution can have de-wetted regions of positive measure, and the Trotter-Kato scheme allows for a simpler proof of existence than in case of Itô noise.