The stochastic thin-film equation: Existence of nonnegative martingale solutions
Benjamin Gess (Bielefeld University, Max Planck Institute)
Manuel Gnann (TU Delft - Analysis)
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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 Itô noise.
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