论文标题
随机Cahn-Hilliard-Navier-Stokes方程，具有动态边界：Martingale弱解决方案，马尔可夫选择
Stochastic Cahn-Hilliard-Navier-Stokes equations with the dynamic boundary: Martingale weak solution, Markov selection
论文作者
论文摘要
建立了在平滑界面中由乘法噪声驱动的2D和3D随机Cahn-Hilliard-navier-Stokes方程的全局Martingale弱解的存在。特别是，该系统提供了动态边界条件，该条件解释了流体成分与刚性壁之间的相互作用。该证明是由三级近似方案结合了固定点参数和随机紧凑性参数，克服了强烈的非线性，动态边界和随机效应的挑战。然后，我们证明了Markov在F. Flandoli和M. Romito建立的抽象框架之后，几乎可以肯定地选择了Markov。
The existence of global martingale weak solution for the 2D and 3D stochastic Cahn-Hilliard-Navier-Stokes equations driven by multiplicative noise in a smooth bounded domain is established. In particular, the system is supplied with the dynamic boundary condition which accounts for the interaction between the fluid components and the rigid walls. The proof is completed by a three-level approximate scheme combining a fixed point argument and the stochastic compactness argument, overcoming challenges from strong nonlinearity, dynamic boundary and random effect. Then, we prove the existence of an almost surely Markov selection to the associated martingale problem following the abstract framework established by F. Flandoli and M. Romito.
