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

## TL;DR

This paper proves the existence of nonnegative martingale solutions for the stochastic thin-film equation with colored Gaussian Stratonovich noise, introducing a new decomposition method that simplifies analysis and numerical implementation.

## Contribution

It presents a novel Trotter-Kato-type decomposition approach for the stochastic thin-film equation, avoiding interface potentials and handling de-wetted regions.

## Key findings

- Existence of nonnegative weak (martingale) solutions established.
- A new numerical scheme based on the decomposition is proposed.
- Simplified proof of existence compared to Itô noise cases.

## 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.