  In this paper, we consider the viscous, incompressible, nonlinear Boussinesq
system in two and three spatial dimension. We study the existence and
regularity of solutions to the Boussinesq system with nonhomogeneous boundary
conditions for which the normal component for the velocity is not necessary
equal to zero. We establish the existence of global weak solutions to the
three-dimensional instationary nonlinear Boussinesq system but without any
smallness assumption on the initial and boundary conditions.
