Boussinesq system with non-homogeneous boundary conditions

Abstract

A classical stationary Boussinesq system with non-homogeneous Dirichlet boundary conditions in a bounded domain Ω ⊂ R 3 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 L p -theory. Uniqueness of the very weak solution is proved under a small data assumption.