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In this article, we derive a large deviation principle for a stochastic 2D Cahn–Hilliard–Navier–Stokes system with a multiplicative noise of Lévy-type. The model consists of the Navier–Stokes equations for the velocity, coupled with a Cahn–Hilliard system for the order (phase) parameter. The proof is based on the weak convergence method introduced by Budhiraja, Dupuis and Maroulas in [Ann. Inst. Henri Poincaré Probab. Stat. 47 (2011) 725–747].

Large deviation principles for a 2D stochastic Cahn–Hilliard–Navier–Stokes driven by jump noise