Lp theory for Boussinesq system with Dirichlet boundary conditions. Issue 1 (25th January 2019) - Acevedo, Paul; Amrouche, Chérif; Conca, Carlos
ABSTRACT: We consider the stationary Boussinesq system with non-homogeneous Dirichlet boundary conditions in a bounded domainΩ ⊂ R 3 of classC 1, 1 with a possibly disconnected boundary. We prove the existence of weak solutions inW 1, p ( Ω ), strong solutions inW 2, p ( Ω ) and very weak solutions inL p ( Ω ) 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.