On the weak solutions to a 3D stochastic Cahn–Hilliard–Navier–Stokes model
Article
Tachim Medjo, T. (2020). On the weak solutions to a 3D stochastic Cahn–Hilliard–Navier–Stokes model
. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 71(1), 10.1007/s00033-019-1237-5
Tachim Medjo, T. (2020). On the weak solutions to a 3D stochastic Cahn–Hilliard–Navier–Stokes model
. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 71(1), 10.1007/s00033-019-1237-5
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.
