The non-Lipschitz stochastic Cahn–Hilliard–Navier–Stokes equations in two space dimensions
Chengfeng Sun, Qianqian Huang, Hui Liu · Stochastics and Dynamics · 2021
The stochastic two-dimensional Cahn–Hilliard–Navier–Stokes equations under non-Lipschitz conditions are considered. This model consists of the Navier–Stokes equations controlling the velocity and the Cahn–Hilliard model controlling the phase parameters. By iterative techniques, a priori estimates and weak convergence method, the existence and uniqueness of an energy weak solution to the equations under non-Lipschitz conditions have been obtained.