Abstract
We study in this article a stochastic version of a coupled Allen-Cahn-Navier-Stokes model on a bounded domain of . The model consists of the Navier-Stokes equations for the velocity, coupled with an Allen-Cahn model for the order (phase) parameter. We prove the existence and uniqueness of a local maximal strong solution when the initial data takes values in . Moreover in the two-dimensional case, we prove that our solution is global.
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