We investigate a stochastic 2D Cahn-Hilliard-Navier-Stokes system with a multiplicative noise of Lvy type. The model consists of the Navier-Stokes equations for the velocity, coupled with a Cahn-Hilliard system for the order (phase) parameter. We prove that the system has a unique global strong solution and we derive some a priori estimates for the solution.
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Deugoué et al. (2019) studied this question.
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