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On the existence and uniqueness of solution to a stochastic 2D Allen–Cahn–Navier–Stokes model

Theodore Tachim Medjo

Department of Mathematics, Florida International University, MMC, Miami, Florida 33199, USA

https://doi.org/10.1142/S0219493719500072Cited by:12 (Source: Crossref)

Abstract

We study, in this paper, a stochastic version of a coupled Allen–Cahn–Navier–Stokes model in a two-dimensional (2D) bounded domain. The model consists of the Navier–Stokes equations (NSEs) for the velocity, coupled with a Allen–Cahn model for the order (phase) parameter. We prove the existence and the uniqueness of a variational solution.

Keywords:

AMSC: 35R60, 35Q35, 60H15, 76M35, 86A05

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