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

TL;DR

This paper proves the existence of an invariant measure and global solutions for 2D stochastic Cahn-Hilliard-Navier-Stokes equations with multiplicative noise, advancing understanding of their long-term behavior.

Contribution

It establishes the existence of invariant measures and global solutions for these complex stochastic PDEs using advanced probabilistic methods.

Findings

Invariant measure exists in $L_x^2\times H^1$ space.

Global pathwise solutions are proven to exist.

Method extends to equations with multiplicative noise.

Abstract

Using the Maslowski and Seidler method, the existence of invariant measure for 2-dimensional stochastic Cahn-Hilliard-Navier-Stokes equations with multiplicative noise is proved in state space $L_x^2\times H^1$, working with the weak topology. Also, the existence of global pathwise solution is investigated using the stochastic compactness argument.