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September  2010, 3(3): 371-408. doi: 10.3934/dcdss.2010.3.371

Existence of global weak solutions to Fokker-Planck and Navier-Stokes-Fokker-Planck equations in kinetic models of dilute polymers

John W. Barrett 1, and  Endre Süli 2,

1. 

Department of Mathematics, Imperial College, London SW7 2AZ, United Kingdom
2. 

Mathematical Institute, University of Oxford, Oxford OX1 3LB, United Kingdom

Received  November 2009 Revised  January 2010 Published  May 2010

This survey paper reviews recent developments concerning the existence of global weak solutions to Fokker-Planck equations with unbounded drift terms, and coupled Navier-Stokes-Fokker-Planck systems of partial differential equations, that arise in finitely extensible nonlinear elastic (FENE) type kinetic models of incompressible dilute polymeric fluids in the case of general noncorotational flow.
Keywords: Fokker-Planck equation., Navier-Stokes equation, Existence of weak solutions, kinetic theory, dilute polymer.
Mathematics Subject Classification: Primary: 35Q30, 76A05, 76D03; Secondary: 82C31, 82D6.
Citation: John W. Barrett, Endre Süli. Existence of global weak solutions to Fokker-Planck and Navier-Stokes-Fokker-Planck equations in kinetic models of dilute polymers. Discrete and Continuous Dynamical Systems - S, 2010, 3 (3) : 371-408. doi: 10.3934/dcdss.2010.3.371
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