### Abstract

Original language | English |
---|---|

Pages (from-to) | 3217–3241 |

Number of pages | 25 |

Journal | SIAM Journal on Mathematical Analysis (SIMA) |

Volume | 44 |

Issue number | 5 |

DOIs | |

Publication status | Published - 10 Sep 2012 |

### Fingerprint

### Keywords

- liquid crystals
- Landau--de Gennes
- Ginzburg--Landau
- low-temperature limit
- radial symmetry
- radial hedgehog
- uniaxiality
- biaxiality
- instability
- asymptotic analysis

### Cite this

*SIAM Journal on Mathematical Analysis (SIMA)*,

*44*(5), 3217–3241. https://doi.org/10.1137/110856861

}

*SIAM Journal on Mathematical Analysis (SIMA)*, vol. 44, no. 5, pp. 3217–3241. https://doi.org/10.1137/110856861

**Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals.** / Henao, Duvan; Majumdar, Apala.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals

AU - Henao, Duvan

AU - Majumdar, Apala

PY - 2012/9/10

Y1 - 2012/9/10

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.

KW - liquid crystals

KW - Landau--de Gennes

KW - Ginzburg--Landau

KW - low-temperature limit

KW - radial symmetry

KW - radial hedgehog

KW - uniaxiality

KW - biaxiality

KW - instability

KW - asymptotic analysis

U2 - 10.1137/110856861

DO - 10.1137/110856861

M3 - Article

VL - 44

SP - 3217

EP - 3241

IS - 5

ER -