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

Abstract

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.