期刊
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
卷 44, 期 5, 页码 3217-3241出版社
SIAM PUBLICATIONS
DOI: 10.1137/110856861
关键词
liquid crystals; Landau-de Gennes; Ginzburg-Landau; low-temperature limit; radial symmetry; radial hedgehog; uniaxiality; biaxiality; instability; asymptotic analysis
资金
- New Frontiers in the Mathematics of Solids-OxMOS Research Programme
- King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04]
- FONDECYT Iniciacion project from the Chilean Ministry of Education [11110011]
- EPSRC [EP/J001686/1]
- Keble research fellowship
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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