Large deviation for a 3D globally modified Cahn–Hilliard–Navier–Stokes model under random influences

Abstract

In this article, we derive a large deviation principle of the strong solution of the 3D globally modified Cahn–Hilliard–Navier–Stokes model under random influences. The model consists of the stochastic globally modified 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 Budhiraja et al. (2011) and based on a variational representation on infinite-dimensional Brownian motion.