Agnieszka Swierczewska-Gwiazda, University of Warsaw, Warszawa, Poland Joint work with Miroslav Bulícek, Piotr Gwiazda, and Endre Süli We will discuss the problem of existence of solutions to the model of the flow of polymeric fluids. The modelling is related with the coupling of equations describing the evolution of macroscopic quantities (like velocity, pressure and eventually also density and temperature) with an additional equation describing the microscopic structure. The influence of the processes of polymerization and fragmentation will be accounted through the dependence of viscosity on the level of polymerization and/or appearance of the extra stress tensor. We concentrate on a dilute solution of polymer chains suspended in a non-Newtonian solvent which can be convected by the macroscopic velocity field, and are also subject to polymerization and fragmentation processes. In a consequence we consider the generalized Navier-Stokes equations coupled with size-structured equations.