Mathematical analysis of the stabilization of lamellar phases by a shear stress
ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 239-267.

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.

DOI : https://doi.org/10.1051/cocv:2002010
Classification : 35B35,  35Q35,  76E05,  76U05
Mots clés : stabilization, shear stress, Couette system, global solution
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author = {Torri, V.},
title = {Mathematical analysis of the stabilization of lamellar phases by a shear stress},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {239--267},
publisher = {EDP-Sciences},
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url = {http://www.numdam.org/articles/10.1051/cocv:2002010/}
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Torri, V. Mathematical analysis of the stabilization of lamellar phases by a shear stress. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 239-267. doi : 10.1051/cocv:2002010. http://www.numdam.org/articles/10.1051/cocv:2002010/

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