TY - JOUR
T1 - Global well-posedness for 2D polymeric fluid models and growth estimate
AU - Masmoudi, Nader
AU - Zhang, Ping
AU - Zhang, Zhifei
N1 - Funding Information:
Nader Masmoudi is partially supported by and NSF grant DMS 0703145. This work was carried out when Ping Zhang visited Courant Institute of New York University. He would like to thank the hospitality of the Institute. Ping Zhang is partially supported by NSF of China under Grant 10525101 and 10421101, National 973 project and the innovation grant from Chinese Academy of Sciences; and Zhifei Zhang is supported by NSF of China under Grant 10601002.
PY - 2008/7/15
Y1 - 2008/7/15
N2 - 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.
AB - 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.
KW - Global well-posedness
KW - Micro-macro interactions
KW - Navier-Stokes equations
KW - Nonlinear Fokker-Planck equations
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U2 - 10.1016/j.physd.2008.03.020
DO - 10.1016/j.physd.2008.03.020
M3 - Article
AN - SCOPUS:44649098150
SN - 0167-2789
VL - 237
SP - 1663
EP - 1675
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 10-12
ER -