  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).
