The stochastic thin-film equation: existence of nonnegative martingale solutions
Probability
2022-08-02 v2 Analysis of PDEs
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 It\^o noise.
Keywords
Cite
@article{arxiv.1904.08951,
title = {The stochastic thin-film equation: existence of nonnegative martingale solutions},
author = {Benjamin Gess and Manuel V. Gnann},
journal= {arXiv preprint arXiv:1904.08951},
year = {2022}
}
Comments
38 pages, revised version, nonnegativity proof changed, details to time regularity and interpolation of operators added