We consider the viscous, incompressible, nonlinear Boussinesq system. 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 a global weak solutions to the three-dimensional instationary nonlinear Boussinesq system but without any smallness assumption on the initial and boundary conditions.