Nonstationary flows with viscous heating effects

The system of equations describing a nonstationary flow of a quasi-newtonian fluid, with temperature dependent viscosity and with the viscous heating, is considered. Existence of at least one weak solution is proved, i.e. we get existence of at least one velocity field having finite energy and existence of a nonnegative temperature field. Its regularity is a consequence of the nonnegative forcing term generated by the viscous heating and being only integrable