Symmetry of Uniaxial Global Landau--de Gennes Minimizers in the Theory of Nematic Liquid Crystals

Duvan Henao, Apala Majumdar

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15 Scopus citations

Abstract

We extend the recent radial symmetry results by Pisante [J. Funct. Anal., 260 (2011), pp. 892-905] and Millot and Pisante [J. Eur. Math. Soc. (JEMS), 12 (2010), pp. 1069- 1096] (who show that the equivariant solutions are the only entire solutions of the three-dimensional Ginzburg-Landau equations in superconductivity theory) to the Landau-de Gennes framework in the theory of nematic liquid crystals. In the low temperature limit, we obtain a characterization of global Landau-de Gennes minimizers, in the restricted class of uniaxial tensors, in terms of the well-known radial-hedgehog solution. We use this characterization to prove that global Landau-de Gennes minimizers cannot be purely uniaxial for sufficiently low temperatures. Copyright © by SIAM.
Original languageEnglish (US)
Pages (from-to)3217-3241
Number of pages25
JournalSIAM Journal on Mathematical Analysis
Volume44
Issue number5
DOIs
StatePublished - Jan 2012
Externally publishedYes

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