On the stochastic nonlocal Cahn-Hilliard Navier-Stokes model with singular potential

In this paper, we consider a stochastic version of a nonlocal Cahn-Hilliard-Navier-Stokes model with a singular potential in a bounded domain of R ^d, d=2,3. The system describes the motion of an incompressible isothermal mixture of two (partially) immiscible fluids under random influences. We prove the existence of a global weak martingale solution. The proof relies on a splitting up method, which is a numerical scheme based on the method of fractional steps. In the two dimensional case, we also prove the pathwise uniqueness of the solution.