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# Dynamics of Partial Differential Equations

## Volume 17 (2020)

### Number 1

### On the strong solutions for a stochastic 2D nonlocal Cahn–Hilliard–Navier–Stokes model

Pages: 19 – 60

DOI: https://dx.doi.org/10.4310/DPDE.2020.v17.n1.a2

#### Authors

#### Abstract

We study in this article a stochastic version of a well-known diffuse interface model. The model consists of the Navier–Stokes equations for the average velocity, nonlinearly coupled with a nonlocal Cahn–Hilliard equation for the order (phase) parameter. The system describes the evolution of an incompressible isothermal mixture of binary fluids excited by random forces in a two dimensional bounded domain. For a fairly general class of random forces, we prove the existence and uniqueness of a variational solution.

#### Keywords

Navier–Stokes equations, nonlocal Cahn–Hilliard equations, incompressible binary fluids, variational solutions, weak solutions

#### 2010 Mathematics Subject Classification

Primary 35-xx, 60-xx. Secondary 76-xx, 86-xx.

Received 11 February 2019

Published 18 February 2020