Study of the Quasi-Static Norton-Hoff Heat Problem

We are interested in the study of a quasistatic visco-plastic flow with thermal effects. The fluid motion is governed by the incompressible Norton-Hof- f model coupled with the dynamic heat equation whose the dissipation mecanicha- l power is the source term. The viscosity of the fluid is modeled by the Arrhenuis law.One of the principal aims of this paper is to prove an existence result to the considered problem and the compactness of the solutions set.