  The aim of this article is to study a nonlinear system modeling a
Non-Newtonian fluid of polymer aqueous solutions. We are interested here in the
existence of weak solutions for the stationary problem in a bounded plane
domain or in two-dimensional exterior domain. Due to the third order of
derivatives in the non-linear term, it's difficult to obtain solution
satisfying energy inequality. But with a good choice of boundary conditions, an
adapt special basis and the use of the good properties of the trilinear form
associated to the non-linear term, we obtain energy solutions. The problem in
bounded domain is treated and the more difficult problem on non bounded domain
too.
