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

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.

38 pages, revised version, nonnegativity proof changed, details to time regularity and interpolation of operators added

References in corpus (5)

• SPDE in Hilbert Space with Locally Monotone Coefficients
• The Navier-slip thin-film equation for 3D fluid films: existence and uniqueness
• The thin film equation close to self-similarity
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Cited by in corpus (3)

• Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise
• Existence of nonnegative solutions to stochastic thin-film equations in two space dimensions
• The Cox-Voinov law for traveling waves in the partial wetting regime