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arXiv · 1904.08951

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

Benjamin Gess·Manuel V. Gnann
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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.

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Benjamin Gess, Manuel V. Gnann. 2019-04-18. The stochastic thin-film equation: existence of nonnegative martingale solutions. https://doi.org/10.1016/j.spa.2020.07.013

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