TY - JOUR
T1 - Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals
AU - Henao, Duvan
AU - Majumdar, Apala
N1 - A Corrigendum to this article was published in SIAM Journal of Mathematical Analysis, 45(6), 3872-3874, http://dx.doi.org/10.1137/130928790.
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84868346795&partnerID=8YFLogxK
UR - http://dx.doi.org/10.1137/110856861
U2 - 10.1137/110856861
DO - 10.1137/110856861
M3 - Article
SN - 0036-1410
VL - 44
SP - 3217
EP - 3241
JO - SIAM Journal on Mathematical Analysis (SIMA)
JF - SIAM Journal on Mathematical Analysis (SIMA)
IS - 5
ER -