Barrett, John W. and Suli, Endre (2006) Existence of global weak solutions to kinetic models for dilute polymers. Technical Report. Unspecified. (Submitted)

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Abstract
We study the existence of globalintime weak solutions to a coupled microscopicmacroscopic beadspring model which arises from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible NavierStokes equations in a bounded domain in two or three space dimensions, for the velocity and the pressure of the fluid, with an elastic extrastress tensor as righthand side in the momentum equation. The extrastress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function which satisfies a FokkerPlanck type parabolic equation, a crucial feature of which is the presence of a centreofmass diffusion term. The anisotropic Friedrichs mollifiers, which naturally arise in the course of the derivation of the model in the Kramers expression for the extra stress tensor and in the drag term in the FokkerPlanck equation, are replaced by isotropic Friedrichs mollifiers. We establish the existence of globalintime weak solutions to the model for a general class of springforcepotentials including in particular the widely used FENE (Finitely Extensible Nonlinear Elastic) potential. We justify also, through a rigorous limiting process, certain classical reductions of this model appearing in the literature which exclude the centreofmass diffusion term from the FokkerPlanck equation on the grounds that the diffusion coefficient is small relative to other coefficients featuring in the equation. In the case of a corotational drag term we perform a rigorous passage to the limit as the Friedrichs mollifiers in the Kramers expression and the drag term converge to identity operators.
Item Type:  Technical Report (Technical Report) 

Subjects:  O  Z > Statistical mechanics, structure of matter D  G > Fluid mechanics H  N > Numerical analysis 
Research Groups:  Numerical Analysis Group 
ID Code:  1109 
Deposited By:  Lotti Ekert 
Deposited On:  11 May 2011 09:57 
Last Modified:  29 May 2015 18:48 
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