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Large deviation for a 2D Allen–Cahn–Navier–Stokes model under random influences

In this article, we derive a large deviation principle for a 2D Allen–Cahn–Navier–Stokes model under random influences. The model consists of the Navier–Stokes equations for the velocity, coupled with an Allen–Cahn equation for the order (phase) parameter. The proof relies on the weak convergence method that was introduced in (Ann. Inst. Henri Poincaré Probab. Stat. 47 (2011) 725–747) and based on a variational representation on infinite-dimensional Brownian motion.