SYMMETRY OF UNIAXIAL GLOBAL LANDAU-DE GENNES MINIMIZERS IN THE THEORY OF NEMATIC LIQUID CRYSTALS
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Date
2012
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SIAM PUBLICATIONS
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.
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Keywords
liquid crystals, Landau-de Gennes, Ginzburg-Landau, low-temperature limit, radial symmetry, radial hedgehog, uniaxiality, biaxiality, instability, asymptotic analysis, MINIMIZATION, REGULARITY