Dynamics of Partial Differential Equations
Volume 17 (2020)
On the strong solutions for a stochastic 2D nonlocal Cahn–Hilliard–Navier–Stokes model
Pages: 19 – 60
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