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The aim of this article is to study a nonlinear system modeling aNon-Newtonian fluid of polymer aqueous solutions. We are interested here in theexistence of weak solutions for the stationary problem in a bounded planedomain or in two-dimensional exterior domain. Due to the third order ofderivatives in the non-linear term, it's difficult to obtain solutionsatisfying energy inequality. But with a good choice of boundary conditions, anadapt special basis and the use of the good properties of the trilinear formassociated to the non-linear term, we obtain energy solutions. The problem inbounded domain is treated and the more difficult problem on non bounded domaintoo.

Energy solutions for polymer aqueous solutions in two dimension