Existence of a solution to the stochastic nonlocal Cahn-Hilliard Navier-Stokes model via a splitting-up method

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 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.