Symmetry of Uniaxial Global Landau--de Gennes Minimizers in the Theory of Nematic Liquid Crystals
KAUST Grant NumberKUK-C1-013-04
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AbstractWe 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.
CitationHenao D, Majumdar A (2012) Symmetry of Uniaxial Global Landau--de Gennes Minimizers in the Theory of Nematic Liquid Crystals. SIAM J Math Anal 44: 3217–3241. Available: http://dx.doi.org/10.1137/110856861.
SponsorsA.M. would like to thank the Oxford Centre for Collaborative Applied Mathematics for its hospitality over the months, August-October 2012, during which this work was completed. Part of this work was carried out during D.H.'s visit to the Oxford Centre for Collaborative Applied Mathematics, whose hospitality is gratefully acknowledged. We also thank the New Frontiers in the Mathematics of Solids-OxMOS Research Programme for having financially supported this visit. We are indebted finally to Adriano Pisante for his reading of the manuscript and for his valuable comments, which helped to improve the final version of the paper.Received by the editors November 28, 2011; accepted for publication June 27, 2012; published electronically September 11, 2012. This publication was based on work supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).Facultad de Matematicas, Pontificia Universidad Catolica de Chile, Casilla 306, Correo 22, Santiago, Chile (email@example.com). This author's research is supported by FONDECYT Iniciacion project 11110011 from the Chilean Ministry of Education.Department of Mathematical Sciences, University of Bath, BA2 7AY, UK (Apala.Majumdar@maths.ox.ac.uk). This author's research is supported by EPSRC career acceleration fellowship EP/J001686/1 and a Keble research fellowship.