Mathematical analysis of the stabilization of lamellar phases by a shear stress

V. Torri

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 7, page 239-267
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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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 7 (2010): 239-267. <http://eudml.org/doc/90620>.

@article{Torri2010,
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. },
author = {Torri, V.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Stabilization; shear stress; Couette system; global solution.; global solution; energy estimates; local existence},
language = {eng},
month = {3},
pages = {239-267},
publisher = {EDP Sciences},
title = { Mathematical analysis of the stabilization of lamellar phases by a shear stress },
url = {http://eudml.org/doc/90620},
volume = {7},
year = {2010},
}

TY - JOUR
AU - Torri, V.
TI - Mathematical analysis of the stabilization of lamellar phases by a shear stress
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 7
SP - 239
EP - 267
AB - 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.
LA - eng
KW - Stabilization; shear stress; Couette system; global solution.; global solution; energy estimates; local existence
UR - http://eudml.org/doc/90620
ER -

References

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  10. J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod (1969).  
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  13. R. Temam, Infinite-dimensional dynamical systems in mechanics and physics. Springer-Verlag, Appl. Math. Sci.68 (1997).  Zbl0871.35001

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