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Mathematical analysis of the stabilization of lamellar phasesby a shear stress

Published online by Cambridge University Press:  15 September 2002

V. Torri
V. Torri*
Affiliation:
Mathématiques Appliquées de Bordeaux, Université de Bordeaux 1 et UMR 5466 du CNRS, 351 cours de la Libération, 33405 Talence Cedex, France; torri@math.u-bordeaux.fr.
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Abstract

We consider a 2D mathematical model describing the motion of a solution of surfactants submitted to a high shear stress in a Couette-Taylor system. We are interested in a stabilization process obtained thanks to the shear. We prove that, if the shear stress is large enough, there exists global in time solution for small initial data and that the solution of the linearized system (controlled by a nonconstant parameter) tends to 0 as t goes to infinity. This explains rigorously some experiments.

Keywords

Stabilizationshear stressCouette systemglobal solution.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 7 , 2002 , pp. 239 - 267
Copyright
© EDP Sciences, SMAI, 2002

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