Abstract
We study the global existence of smooth solutions near the equilibrium to a coupled microscopic-macroscopic FENE dumbbell model which arises from the kinetic theory of diluted solutions of polymeric liquids with noninteracting polymer chains.
Similar content being viewed by others
References
Bird, R. B., Curtis, C. F., Armstrong, R. C., Hassager, O.: Dynamics of Polymeric Liquids, Volume 2: Kinetic Theory, Weiley Interscience, New York, 1987
Doi, M., Edwards, S. F.: The Theory of Polymer Dynamics, Oxford Science Publication, 1986
Jourdain, B., Leliévre, T., Le Bris, C.: Existence of solution for a micro-macro model of polymeric fluid: the FENE model. J. Funct. Anal., 209, 162–193 (2004)
Weinan, E, Li, T. J., Zhang, P. W.: Well-posedness for the dumbbell model of polymeric fluids. Comm. Math. Phys.. 248(2), 409–427 (2004)
Zhang, H., Zhang, P. W.: Local existence for the FENE-dumbbell model of polymeric fluids, Arch. Ration. Mech. Anal., 181, 373–400 (2006)
Renardy, M.: An existence theorem for model equations resulting from kinetic theories of polymer solutions, SIAM J. Math. Anal., 22, 313–327 (1991)
Constantin, P., Fefferman, C., Titi, E., Zarnescu, A.: Regularity for coupled two-dimensional nonlinear Fokker-Planck and Navier-Stokes systems, Comm. Math. Phys., 270, 789–811 (2007)
Barrett, J. W., Schwab, C., Süli, E.: Existence of global weak solutions for some polymeric flow models. Math. Models Methods Appl. Sci., 15, 939–983 (2005)
Lin, F., Liu, C., Zhang, P.: On a Micro-Macro model for polymeric fluids near equilibrium. Comm. Pure Appl. Math., 60, 838–866 (2007)
Lin, F., Liu, C., Zhang, P.: On hydrodynamics of viscoelastic fluids. Comm. Pure Appl. Math., 58, 1437–1471 (2005)
Filippas, S., Maz’ya, V., Tertikas, A.: Critical Hardy-Sobolev inequalities. J. Math. Pures Appl., 87(9), 37–56 (2007)
Lin, F.: On the Dirichelet problem for minimal graphs in hyperbolic space. Invent. Math., 96, 593–612 (1989)
Kohn, J. J., Nirenberg, L.: Degenerated ellptic-parabolic equations of second order. Comm. Pure Appl. Math., 20, 797–872 (1967)
Matskewich, T., Sobolevskii, P. E.: The sharp constant in Hardy’s inequality for complement of bounded domain. Nonlinear Anal., 33, 105–120 (1998)
Author information
Authors and Affiliations
Corresponding author
Additional information
Lin is partially supported by NSF Grant DMS-0201443; Zhang is partially supported by NSF of China under Grants 10525101 and 10421101, 973 Project and the Innovation Grant from Chinese Academy of Sciences
Rights and permissions
About this article
Cite this article
Lin, F.H., Zhang, P. The FENE dumbbell model near equilibrium. Acta. Math. Sin.-English Ser. 24, 529–538 (2008). https://doi.org/10.1007/s10114-007-1034-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-007-1034-5