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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 CouetteTaylor 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 goes to infinity. This explains rigorously some experiments.
@article{COCV_2002__7__239_0,
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},
volume = {7},
year = {2002},
doi = {10.1051/cocv:2002010},
mrnumber = {1925028},
zbl = {1023.35013},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002010/}
}
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 PY - 2002 SP - 239 EP - 267 VL - 7 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002010/ DO - 10.1051/cocv:2002010 LA - en ID - COCV_2002__7__239_0 ER -
%0 Journal Article %A Torri, V. %T Mathematical analysis of the stabilization of lamellar phases by a shear stress %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 239-267 %V 7 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2002010/ %R 10.1051/cocv:2002010 %G en %F COCV_2002__7__239_0
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
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