The Mathematical Institute, University of Oxford, Eprints Archive

Existence of Global Weak Solutions for Some Polymeric Flow Models

Barrett, John W. and Schwab, Christoph and Suli, Endre (2004) Existence of Global Weak Solutions for Some Polymeric Flow Models. Technical Report. Unspecified. (Submitted)

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Abstract

We study the existence of global-in-time weak solutions to a coupled microscopic-macroscopic bead-spring model which arises from the kinetic theory of diluted solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier-Stokes equations in a bounded domain for the velocity and the pressure of the fluid, with an extra-stress tensor as right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function which satisfies a Fokker-Planck type degenerate parabolic equation. Upon appropriate smoothing of the convective velocity field in the Fokker-Planck equation, and in some circumstances, of the extra-stress tensor, we establish the existence of global-in-time weak solutions to this regularised bead-spring model for a general class of spring-force-potentials including in particular the widely used FENE (Finitely Extensible Nonlinear Elastic) model.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1166
Deposited By:Lotti Ekert
Deposited On:14 May 2011 08:44
Last Modified:14 May 2011 08:44

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