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 Ito noise.

中文翻译：

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随机薄膜方程：非负鞅解的存在性

我们考虑在一维空间中具有彩色高斯 Stratonovich 噪声的随机薄膜方程，并建立非负弱（鞅）解的存在性。该构造基于将 Trotter-Kato 类型分解为确定性和随机进化，从而产生易于实现的数值算法。与之前的工作相比，不需要包含界面电位，初始数据和解决方案可以具有正测量的去湿区域，并且与 Ito 噪声的情况相比，Trotter-Kato 方案允许更简单的存在证明。