A convergence result for an iterative method for the equations of a stationary quasi-Newtonian flow with temperature dependent viscosity

We study a system of equations describing the stationary and incompressible flow of a quasi-Newtonian fluid with temperature dependent viscosity and with a viscous heating. An algorithm wich decouples the calculation of the temperature T and the velocity and the pressure (v, p) is presented. It consists in solving iteratively a problem with a nonlinear Stokes's operator for v and p and the Poisson's equation with right-hand side in L-1 for T. We prove, using the method of pseudomonotonicity and under a regularity assumption of Meyers type that the mapping defined by this scheme is a contraction for sufficiently small data. (C) Elsevier; Paris.