Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 237, Issue 10-12, Pages 1663-1675Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2008.03.020
Keywords
nonlinear Fokker-Planck equations; Navier-Stokes equations; micro-macro interactions; global well-posedness
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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. (c) 2008 Elsevier B.V. All rights reserved.
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