The Periodic Initial Value Problem and Initial Value Problem for the Non-Newtonian Boussinesq Approximation

The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds more and more frequent use in geological practice. In this article, we consider the periodic initial value problem and initial value problem for the non-Newtonian Boussinesq equations describing the behavior of flows of an incompressable viscous fluid in processes where the thermal effects play an essential role. The existence of weak solution is proved for p ≥2, its uniqueness and regularity for p>(1+2n/(n+2)).