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) |
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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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