Global well-posedness for 2D polymeric fluid models and growth estimate

Motivated by [P. Constantin, N. Masmoudi, Global well-posedness for a Smoluchowski equation coupled with Navier–Stokes equations in 2D, Comm. Math. Phys. 278 (2008) 179–191; F. Lin, Ping Zhang, Zhifei Zhang, On the global existence of smooth solution to the 2-D FENE dumbbell model, Comm. Math. Phys. 277 (2008) 531–553], we prove the global existence of smooth solutions to a coupled microscopic–macroscopic model for polymeric fluid in 2D under the co-rotational assumption. Furthermore, we provide an estimate on the time growth of these solutions. Our method is general and can be applied to the co-rotational FENE model and to the rod-like model without the co-rotational assumption.