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Analysis of a viscosity model for concentrated polymers

Mathematical Institute, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovská 83, 186 75 Prague, Czech Republic

E-mail Address: mbul8060@karlin.mff.cuni.cz

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Piotr Gwiazda

Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland

E-mail Address: pgwiazda@mimuw.edu.pl

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Endre Süli

Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, UK

E-mail Address: endre.suli@maths.ox.ac.uk

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Agnieszka Świerczewska-Gwiazda

Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland

E-mail Address: aswiercz@mimuw.edu.pl

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https://doi.org/10.1142/S0218202516500391Cited by:1 (Source: Crossref)

Abstract

The paper is concerned with a class of mathematical models for polymeric fluids, which involves the coupling of the Navier–Stokes equations for a viscous, incompressible, constant-density fluid with a parabolic–hyperbolic integro-differential equation describing the evolution of the polymer distribution function in the solvent, and a parabolic integro-differential equation for the evolution of the monomer density function in the solvent. The viscosity coefficient, appearing in the balance of linear momentum equation in the Navier–Stokes system, includes dependence on the shear rate as well as on the weight-averaged polymer chain length. The system of partial differential equations under consideration captures the impact of polymerization and depolymerization effects on the viscosity of the fluid. We prove the existence of global-in-time, large-data weak solutions under fairly general hypotheses.

Communicated by F. Brezzi

Keywords:

AMSC: 35Q35, 76D03, 35M13, 35Q92

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