二维随机薄膜方程的鞅解
Martingale solutions to the stochastic thin-film equation in two dimensions
摘要：
我们构造解决方案的随机薄膜方程与二次流动性和Stratonovich梯度噪声在物理上相关的尺寸$d=2$，并允许特别是与非完全支持的解决方案。该构造依赖于Trotter-Kato时间分裂方案，该方案最近在$d=1$中采用。由于更高的空间维度的额外的分析挑战，克服使用$α$ -熵估计和相应的紧密性参数。
英文摘要：
We construct solutions to the stochastic thin-film equation with quadratic mobility and Stratonovich gradient noise in the physically relevant dimension $d=2$ and allow in particular for solutions with non-full support. The construction relies on a Trotter-Kato time-splitting scheme, which was recently employed in $d=1$. The additional analytical challenges due to the higher spatial dimension are overcome using $α$-entropy estimates and corresponding tightness arguments.
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