Global well-posedness for a Navier-Stokes-Cahn-Hilliard-Boussinesq system with singular potential

We study an initial-boundary value problem for a two-dimensional Navier-Stokes-Cahn-Hilliard-Boussinesq system for a mixture of two incompressible Newtonian fluids caused by thermo-induced Marangoni effect. The singular potential is considered. Given suitable initial and boundary conditions, we prove the existence of global weak solutions and global strong solutions. We also give a criterion of continuous dependence with respect to the initial data (uniqueness).Comment: Key words: Navier-Stokes equations; Cahn-Hilliard equation; Boussinesq equation; singular potential; weak solutions; strong solutions; uniquenes