  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.
