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We provide a new proof for the global well-posedness of systems couplingfluids and polymers in two space dimensions. Compared to the well-knownexisting method based on the losing a priori estimates, our method is moredirect and much simpler. The co-rotational FENE dumbbell model and the couplingSmoluchowski and Navier-Stokes equations are studied as examples to illustrateour main ideas.

Global solutions for micro-macro models of polymeric fluids