Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals

Duvan Henao, Apala Majumdar

Research output: Contribution to journalArticle

15 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)3217–3241
Number of pages25
JournalSIAM Journal on Mathematical Analysis (SIMA)
Volume44
Issue number5
DOIs
Publication statusPublished - 10 Sep 2012

Keywords

  • liquid crystals
  • Landau--de Gennes
  • Ginzburg--Landau
  • low-temperature limit
  • radial symmetry
  • radial hedgehog
  • uniaxiality
  • biaxiality
  • instability
  • asymptotic analysis

Cite this