Solutions faibles H2 pour un modèle de fluide non newtonien

This Note is devoted to the study a non-linear system modelling a flow of a non-Newtonian fluid, namely aqueous polymer solutions. In the present work, we prove a theorem on the existence of weak solutions for the steady-state problem in a bounded or exterior plane domain. A first difficulty is due to the fact that we search these solutions in the natural space given by the energy inequalities. The second difficulty stems from the fact that the non-linear term involves a third-order derivative, whereas its elliptic term is only a Laplace operator. To cite this article: C. Amrouche, E.-H. Ouazar, C. R. Acad. Sci. Paris, Ser. I 341 (2005).