Finite-dimensional description of the long-term dynamics for the 2D Doi-Hess model for liquid crystalline polymers in shear flow
Vukadinovic, J.
Commun. Math. Sci., Tome 6 (2008) no. 1, p. 975-993 / Harvested from Project Euclid
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The existence of inertial manifolds for a Smoluchowski equation arising in the 2D Doi-Hess model for liquid crystalline polymers subjected to a shear flow is investigated. The presence of a non-variational drift term dramatically complicates the long-term dynamics from the variational gradient case, in which it is solely characterized by the steady states. Several transformations are used in order to transform the equation into a form suitable for application of the standard theory of inertial manifolds. A nonlinear and nonlocal transformation developed in Inertial manifolds for a Smoluchowski equation on a circle and Inertial manifolds for a Smoluchowski equation on the unit sphere,, to appear, is used to eliminate the first-order derivative from the micro-micro interaction term. A traveling wave transformation eliminates the first-order derivative from the non-variational term, transforming the equation into a nonautonomous one for which the theory of nonautonomous inertial manifolds applies.
Publié le : 2008-12-15
Classification:  Doi-Hess model,  Smoluchowski equation,  shear flow,  nonautonomous inertial manifolds,  Schrödinger-like equation,  35Kxx,  70Kxx 
@article{1229619679,
     author = {Vukadinovic, J.},
     title = {Finite-dimensional description of the long-term dynamics for the 2D Doi-Hess 
					model for liquid crystalline polymers in shear flow},
     journal = {Commun. Math. Sci.},
     volume = {6},
     number = {1},
     year = {2008},
     pages = { 975-993},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1229619679}
}

Vukadinovic, J. Finite-dimensional description of the long-term dynamics for the 2D Doi-Hess 
					model for liquid crystalline polymers in shear flow. Commun. Math. Sci., Tome 6 (2008) no. 1, pp.  975-993. http://gdmltest.u-ga.fr/item/1229619679/