Boussinesq system with non-homogeneous boundary conditions

A classical stationary Boussinesq system with non-homogeneous Dirichlet boundary conditions in a bounded domain Ω⊂R3Ω⊂R3 is considered in this paper; included is the case of a possibly disconnected boundary. We prove existence of a weak, a strong and a very weak solution in LpLp-theory. Uniqueness of the very weak solution is proved under a small data assumption.