Abstract
ABSTRACTWe consider the stationary Boussinesq system with non-homogeneous Dirichlet boundary conditions in a bounded domain of class with a possibly disconnected boundary. We prove the existence of weak solutions in , strong solutions in and very weak solutions in of the stationary Boussinesq system by assuming that the fluxes of the velocity are sufficiently small. Finally, as it is expected, we obtain the uniqueness of the solution by considering small data.
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