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Existence and stability of steady flows of weakly viscoelastic fluids*

Published online by Cambridge University Press:  14 November 2011

Colette Guillopé  and
Jean-Claude Saut
Colette Guillopé
Affiliation:
Laboratoire d'Analyse Numérique, Bâtiment 425, Université Paris–Sud and C.N.R.S., 91405 Orsay, France
Jean-Claude Saut
Affiliation:
Laboratoire d'Analyse Numérique, Bâtiment 425, Université Paris–Sud and C.N.R.S., 91405 Orsay, France; Mathématiques, Université Paris–Val de Marne, 94010 Creteil Cedex, France
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Synopsis

We consider steady flows of viscoelastic fluids for which the extrastress tensor is given by a differential constitutive equation and is such that the retardation time is large (weakly viscoelastic fluids).

We show the existence of a unique viscoelastic steady flow close to a given Newtonian flow and investigate its linear stability.

As an example, we consider the Bénard problem for viscoelastic fluids and we prove that there exists a nontrivial linearly stable flow of a weakly viscoelastic fluid in a container heated from below.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 119 , Issue 1-2 , 1991 , pp. 137 - 158
Copyright
Copyright © Royal Society of Edinburgh 1991

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