We consider a stochastic diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids under the influence of stochastic external forces in a bounded domain of ##IMG## [http://ej.iop.org/images/0951-7715/33/7/3424/nonab8020ieqn1.gif] {${\mathbb{R}}^{d}$} , d = 2, 3. The model consists of the stochastic Navier–Stokes equations coupled with a nonlocal Cahn–Hilliard equation. We prove the existence of a global weak martingale solution via a numerical scheme based on splitting-up method.

中文翻译：

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通过分解方法求解随机非局部Cahn–Hilliard Navier–Stokes模型的解的存在性

我们考虑一个随机扩散界面模型，该模型描述了在## IMG ##的有界域中，在随机外力的作用下，两种不互溶的流体的不可压缩等温混合物的运动[http://ej.iop.org/images/ 0951-7715 / 33/7/3424 / nonab8020ieqn1.gif] {$ {\ mathbb {R}} ^ {d} $}，d = 2，3。模型由随机的Navier–Stokes方程和非局部方程组成Cahn–Hilliard方程。通过基于分裂方法的数值方案，我们证明了全局弱mar解决方案的存在。