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On the weak solutions to a 3D stochastic Cahn–Hilliard–Navier–Stokes model

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Abstract

We study in this article a stochastic version of a coupled Cahn–Hilliard–Navier–Stokes model in a two- or three-dimensional bounded domain. The model consists of the Navier–Stokes equations for the velocity, coupled with an Cahn–Hilliard model for the order (phase) parameter. We prove the existence of a probabilistic weak solution. The proof relies on a Galerkin approximation as well as some compactness results. In the two-dimensional case, we also derive the uniqueness of the weak solutions.

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  1. Department of Mathematics, Florida International University, DM413B University Park, Miami, Florida, 33199, USA

    Theodore Tachim Medjo

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  1. Theodore Tachim Medjo
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Tachim Medjo, T. On the weak solutions to a 3D stochastic Cahn–Hilliard–Navier–Stokes model. Z. Angew. Math. Phys. 71, 13 (2020). https://doi.org/10.1007/s00033-019-1237-5

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  • DOI: https://doi.org/10.1007/s00033-019-1237-5

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