Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

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

Pages: 371 - 408, Volume 3, Issue 3, September 2010      doi:10.3934/dcdss.2010.3.371

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John W. Barrett - Department of Mathematics, Imperial College, London SW7 2AZ, United Kingdom (email)
Endre Süli - Mathematical Institute, University of Oxford, Oxford OX1 3LB, United Kingdom (email)

Abstract: 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:  Existence of weak solutions, dilute polymer, kinetic theory, Navier-Stokes equation, Fokker-Planck equation.
Mathematics Subject Classification:  Primary: 35Q30, 76A05, 76D03; Secondary: 82C31, 82D60.

Received: November 2009;      Revised: January 2010;      Available Online: May 2010.