On the existence and uniqueness of solution to a stochastic 2D Cahn-Hilliard-Navier-Stokes model

We study in this article a stochastic version of a coupled Cahn-Hilliard-Navier-Stokes model in a two dimensional bounded domain. The model consists of the Navier-Stokes equations for the velocity, coupled with a Cahn-Hilliard model for the order (phase) parameter. We prove the existence and the uniqueness of a variational solution.