Invariant measure for 2D stochastic Cahn–Hilliard–Navier–Stokes equations

Abstract

In this paper, we investigate the stochastic Cahn–Hilliard–Navier–Stokes equations in two-dimensional spaces. Applying the Maslowski–Seidler method, we establish the existence of invariant measure in state space [Formula: see text] with the weak topology. We also prove the existence of global pathwise solutions using the stochastic compactness argument.