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couette system

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Mathematical analysis of the stabilization of lamellar phases by a shear stress
V. Torri
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 7 / 2002

Published online by Cambridge University Press:

15 September 2002, pp. 239-267

Print publication:

2002
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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.