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

Abstract

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.