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


G. Deugoué (Department of Mathematics and Computer Science, University of Dschang, Cameroon)

A. Ndongmo Ngana (Department of Mathematics and Computer Science, University of Dschang, Cameroon)

T. Tachim Medjo (Department of Mathematics and Statistics, Florida International University, Miami, Florida, U.S.A.)


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.


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