Convergence of the solution of the stochastic 3D globally modified Cahn-Hilliard-Navier-Stokes equations

We study in this article the stochastic 3D globally modified Cahn-Hilliard-Navier-Stokes model in a 3D dimensional bounded domain. We prove the existence and uniqueness of strong solutions. Furthermore, we discuss the relation of the stochastic 3D globally modified Cahn-Hilliard-Navier-Stokes equations to the stochastic 3D Cahn-Hilliard-Navier-Stokes equations by proving a convergence theorem, that as the parameter N tends to infinity, a subsequence of solutions of the stochastic 3D globally modified Cahn-Hilliard-Navier-Stokes equations converges to a weak martingale solution of the stochastic 3D Cahn-Hilliard-Navier-Stokes equations.