We can now proceed in precisely the same manner as in section 2 to establish convergence of the iteration scheme.If ro = 0, the operator L[u] as defined above is not coercive and lemma 3.1 does not hold. In this case, we adopt a different procedure. Let i be any positive real number. We apply the operator (u . ' 17) + 2 to (3.3) and obtainWe now seta coercive operator in P(Q) and L[u]-l exists. We can now apply the operator L[u]-l to (3.8), define p = L[u]-l x x ((u * V) + 1) p and set up an iteration scheme in an analogous fashion as before. References 1 M. J. CROCHET and K. WALTERS, Numerical methods in non-Newtonian fluid mechanics, Ann. Rev. Fluid Mech. 15 (1983), 241 -260. 2 H. GIESEKUS, A unified approach to a variety of constitutive models for polymer fluids based on the concept of configuration dependent molecular mobility, Rheol. Acta 21 (19SZ), 386-3375. 3 M. S. GREEN and A. V. TOBOLSRY, A new approach to the theory of relaxing polymeric media, J. Chem. Phys. 14 (1946), 80-100. 4 T. KATO, Perturbation Theory for Linear Operators, Springer, 1966. 5 0. A. LADY~ENSRAYA, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, 1969. 6 A. I. LEONOV, Nonequilihrium thermodynamics and rheology of viscoelastic polymer media, Rheol. Acta 16 (1976), 85-98. 7 A. 5. LODGE, A network theory of flow birefringence and stress in concentrated polymer solutions, Trans. Faraday Sac. 62 (1956), 120-130. 8 111. NIGGEMANN, A model equation for non-Newtonian fluids, Math. Meth. Appl. Sci. S (1981), 200-217. 9 J. G. OLDROYD, Non-Newtonian effects in steady mation of some idealized elasticoviscous liquids, Proc.