Partial Regularity of Weak Solutions of the Stationary 3D-Boussinesq System

In this paper, we study the smoothness of weak solutions of the three-dimensional stationary Boussinesq system describing steady-state motion of viscous heat-convergent Newtonian fluid whose viscosity may depend on the temperature of the fluid. The principal feature of the system under consideration is the occurrence of the dissipative term in the equation of energy balance. This term is equal to the product of the stress and the strain velocity tensors and has a quadratic growth with respect to the gradient of the velocity field. We prove the partial regularity of solutions to this system and give an estimate of the Hausdorff measure of the singular set. Bibliography: 14 titles.