The stochastic thin-film equation: Existence of nonnegative martingale solutions

Benjamin Gess and Manuel V. Gnann

Stochastic Processes and their Applications, 2020, vol. 130, issue 12, 7260-7302

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.

Date: 2020
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DOI: 10.1016/j.spa.2020.07.013

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