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A relaxed model and its homogenization for nematic liquid crystals in composite materials

✍ Scribed by Quan Shen; M. Carme Calderer

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
149 KB
Volume
27
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

We analyse a model for equilibrium configurations of composite systems of nematic liquid crystal with polymer inclusions, in the presence of an external magnetic field. We assume that the system has a periodic structure, and consider the relaxed problem on the unit length constraint of the nematic director field. The relaxation of the Oseen–Frank energy functional is carried out by including bulk as well as surface energy penalty terms, rendering the problem fully non‐linear. We employ two‐scale convergence methods to obtain effective configurations of the system, as the size of the polymeric inclusions tends to zero. We discuss the minimizers of the effective energies for, both, the constrained as well as the unconstrained models. Copyright © 2004 John Wiley & Sons, Ltd.

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## Abstract In [3], L. Berselli showed that the regularity criterion ∇**u** ∈ (0, __T__; **L**^__q__^ (Ω)), for some __q__ ∈ (3/2, + ∞], implies regularity for the weak solutions of the Navier–Stokes equations, being **u** the velocity field. In this work, we prove that such hypothesis on the velo