On a polymeric flow

We study a flow of dilute polymers in a solvent (e.g. water). Hence, we consider the non-Newtonian fluid equation. We also assume that polymers are chain-like molecules consisting of monomers and we take into account the polymerization process. Therefore, the tensor in the non-Newtonian fluid equation is dependent on the solution of the evolutionary equation responsible for the behavior of the particles. We show the existence of the solutions using the renormalization and duality theory for the transport equation and the theory of non-Newtonian fluids.