ON THE DERIVATION OF AVERAGED EQUATIONS D ESCRIBING NON-NEWTONIAN VISCOUS-FLOW THROUGH A THIN SLAB

We consider the non-Newtonian flow through a thin slab, governed by in jection of a fluid. Starting from the 3D incompressible Navier-Stokes system with a nonlinear viscosity, obeying the power law, we consider the limit when thickness E of the slab tends to zero. We find that ave raged velocity obeys a nonlinear filtration law associated to the gene ralized r'-Laplacian of the averaged pressure. On the boundary the nor mal component of averaged velocity is equal to the normal component of the injection velocity average. Finally, we prove the convergence the orem for velocity and pressure in appropriate functional spaces.