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On the IAA version of the Doi–Edwards model versus the K-BKZ rheological model for polymer fluids: A global existence result for shear flows with small initial data†

Published online by Cambridge University Press:  08 January 2016

IONEL SORIN CIUPERCA ,
ARNAUD HEIBIG  and
LIVIU IULIAN PALADE
IONEL SORIN CIUPERCA
Affiliation:
Université de Lyon, CNRS, Institut Camille Jordan UMR 5208, Université Lyon 1, Bât Braconnier, 43 Boulevard du 11 Novembre 1918, F-69622, Villeurbanne, France email: ciuperca@math.univ-lyon.fr
ARNAUD HEIBIG
Affiliation:
INSA-Lyon, Pôle de Mathématiques, Bât. Leonard de Vinci No. 401, 21 Avenue Jean Capelle, F-69621, Villeurbanne, France email: arnaud.heibig@insa-lyon.fr, liviu-iulian.palade@insa-lyon.fr
LIVIU IULIAN PALADE
Affiliation:
INSA-Lyon, Pôle de Mathématiques, Bât. Leonard de Vinci No. 401, 21 Avenue Jean Capelle, F-69621, Villeurbanne, France email: arnaud.heibig@insa-lyon.fr, liviu-iulian.palade@insa-lyon.fr
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Abstract

This paper establishes the existence of smooth solutions for the Doi–Edwards rheological model of viscoelastic polymer fluids in shear flows. The problem turns out to be formally equivalent to a K-BKZ equation but with constitutive functions spanning beyond the usual mathematical framework. We prove, for small enough initial data, that the solution remains in the domain of hyperbolicity of the equation for all t≥0.

Keywords

Doi–Edwards polymer modelK-BKZ viscoelastic fluidshear flowsconvolution operatorevolutionary integro-differential equation

Information

Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 1 , February 2017 , pp. 42 - 90
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

†

Dedicated to Professor Denis Serre, Ecole Normale Supérieure de Lyon, France, on the occasion of his 60th birthday anniversary.

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