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 incompres sible flow of a quasi-Newtonian fluid with temperature dependent visco sity and with a viscous heating. An algorithm wich decouples the calcu lation of the temperature T and the velocity and the pressure (v, p) i s presented. It consists in solving iteratively a problem with a nonli near Stokes's operator for v and p and the Poisson's equation with rig ht-hand side in L-1 for T. We prove, using the method of pseudomonoton icity and under a regularity assumption of Meyers type that the mappin g defined by this scheme is a contraction for sufficiently small data. (C) Elsevier; Paris.