Large deviation for a 2D Cahn-Hilliard-Navier-Stokes model under random influences

Abstract

In this article, we derive a large deviation principle for a 2D Cahn-Hilliard-Navier-Stokes model under random influences. The model consists of the Navier-Stokes equations for the velocity, coupled with a Cahn-Hilliard equation for the order (phase) parameter. The proof relies on the weak convergence method that was introduced in [3–5] and based on a variational representation on infinite-dimensional Brownian motion.