AI 中文总结
研究由输运噪声驱动的两种不可压缩流体混合物的扩散界面模型，在适当假设下证明二维情形全局弱鞅解存在及全局强解路径唯一性，是首个处理相关统一框架的结果。
AI 中文摘要
我们考虑由输运噪声驱动的两种不可压缩流体混合物的扩散界面模型。在适当的抽象假设下，我们证明了全局弱鞅解的存在性以及二维情况下全局强解的路径唯一性。这是第一个解决从Brzeźniak & Motyl和Mikulevicius & Rozovskii的工作中得出的统一框架的结果，用于研究随机偏微分方程。
英文摘要
We consider a diffuse interface model for the mixture of two incompressible fluids driven by transport noise. Under suitable abstract assumptions, we prove the existence of a global weak martingale solution as well as the pathwise uniqueness of a global strong solution in the two dimensional case. This is the first result addressing a unified framework derived from the works by Brze{ź}niak \& Motyl and Mikulevicius \& Rozovskii, on the study of stochastic partial differential equations.
