The Mathematical Institute, University of Oxford, Eprints Archive

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

Henao, D. and Majumdar, A. (2011) Symmetry of uniaxial global Landau-de Gennes minimizers in the
theory of nematic liquid crystals.
SIAM Journal on Mathematical Analysis . (Submitted)

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Abstract

We extend the recent radial symmetry results by Pisante [23] and Millot & Pisante [19] (who show that all entire solutions of the vector-valued Ginzburg-Landau equations in superconductivity theory, in the three-dimensional space, are comprised of the well-known class of equivariant solutions) 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.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1474
Deposited By:Peter Hudston
Deposited On:23 Feb 2012 08:49
Last Modified:23 Feb 2012 08:49

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