On the strong solutions for a stochastic 2D nonlocal Cahn-Hilliard-Navier-Stokes Model
Article
Deugoué, G, Ngana, AN, Medjo, TT. (2020). On the strong solutions for a stochastic 2D nonlocal Cahn-Hilliard-Navier-Stokes Model
. DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 17(1), 19-60. 10.4310/DPDE.2020.v17.n1.a2
Deugoué, G, Ngana, AN, Medjo, TT. (2020). On the strong solutions for a stochastic 2D nonlocal Cahn-Hilliard-Navier-Stokes Model
. DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS, 17(1), 19-60. 10.4310/DPDE.2020.v17.n1.a2
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.
