Global solutions for micro-macro models of polymeric fluids

We provide a new proof for the global well-posedness of systems coupling fluids and polymers in two space dimensions. Compared to the well-known existing method based on the losing a priori estimates, our method is more direct and much simpler. The co-rotational FENE dumbbell model and the coupling Smoluchowski and Navier-Stokes equations are studied as examples to illustrate our main ideas

Global weak solutions for some Oldroyd models

We investigate an evolutive system of non-linear partial differential equations derived from Oldroyd models on Non-Newtonian flows. We prove global existence of weak solutions, in the case of a smooth bounded domain, for general initial data. The results hold true for the periodic case.Comment: Submitte