Nonstationary Flows with Viscous Heating Effects

The system of equations describing a nonstationary ow of a quasi-newtonian uid, 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 eld having nite energy and existence of a nonnegative temperature eld. Its regularity is a consequence of the L 1-forcing term generated by the viscous heating. 1. Introduction In most polymer processing applications the temperature changes are important and cannot be neglected. An example is the manufacture of plastic objects involving processing operations as melting and cooling. It leads to considering the equations of a quasi-Newtonian ow with important viscous dissipation. The starting point for our considerations is the following system of equa