Stability of point defects of degree ±12 in a two-dimensional nematic liquid crystal model

Radu Ignat; Luc Nguyen; Valeriy Slastikov; Arghir Zarnescu

doi:10.1007/s00526-016-1051-2

Stability of point defects of degree ±12 in a two-dimensional nematic liquid crystal model

Radu Ignat^*
, Luc Nguyen
, Valeriy Slastikov
, Arghir Zarnescu

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

30 Citations (Scopus)

282 Downloads (Pure)

Abstract

We study k-radially symmetric solutions corresponding to topological defects of charge k2 for integer k≠ 0 in the Landau-de Gennes model describing liquid crystals in two-dimensional domains. We show that the solutions whose radial profiles satisfy a natural sign invariance are stable when | k| = 1 (unlike the case | k| > 1 which we treated before). The proof crucially uses the monotonicity of the suitable components, obtained by making use of the cooperative character of the system. A uniqueness result for the radial profiles is also established.

Original language	English
Article number	119
Number of pages	33
Journal	Calculus of Variable and Partial Differential Equations
Volume	55
Issue number	5
Early online date	23 Sept 2016
DOIs	https://doi.org/10.1007/s00526-016-1051-2
Publication status	Published - 1 Oct 2016

Keywords

35A15
35B38
49J10
49J30
76A15
82D30

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10.1007/s00526-016-1051-2

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https://arxiv.org/abs/1601.02812

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title = "Stability of point defects of degree ±12 in a two-dimensional nematic liquid crystal model",

abstract = "We study k-radially symmetric solutions corresponding to topological defects of charge k2 for integer k≠ 0 in the Landau-de Gennes model describing liquid crystals in two-dimensional domains. We show that the solutions whose radial profiles satisfy a natural sign invariance are stable when | k| = 1 (unlike the case | k| > 1 which we treated before). The proof crucially uses the monotonicity of the suitable components, obtained by making use of the cooperative character of the system. A uniqueness result for the radial profiles is also established.",

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T1 - Stability of point defects of degree ±12 in a two-dimensional nematic liquid crystal model

AU - Ignat, Radu

AU - Nguyen, Luc

AU - Slastikov, Valeriy

AU - Zarnescu, Arghir

PY - 2016/10/1

Y1 - 2016/10/1

N2 - We study k-radially symmetric solutions corresponding to topological defects of charge k2 for integer k≠ 0 in the Landau-de Gennes model describing liquid crystals in two-dimensional domains. We show that the solutions whose radial profiles satisfy a natural sign invariance are stable when | k| = 1 (unlike the case | k| > 1 which we treated before). The proof crucially uses the monotonicity of the suitable components, obtained by making use of the cooperative character of the system. A uniqueness result for the radial profiles is also established.

AB - We study k-radially symmetric solutions corresponding to topological defects of charge k2 for integer k≠ 0 in the Landau-de Gennes model describing liquid crystals in two-dimensional domains. We show that the solutions whose radial profiles satisfy a natural sign invariance are stable when | k| = 1 (unlike the case | k| > 1 which we treated before). The proof crucially uses the monotonicity of the suitable components, obtained by making use of the cooperative character of the system. A uniqueness result for the radial profiles is also established.

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KW - 35B38

KW - 49J10

KW - 49J30

KW - 76A15

KW - 82D30

UR - https://www.scopus.com/pages/publications/84988805362

U2 - 10.1007/s00526-016-1051-2

DO - 10.1007/s00526-016-1051-2

M3 - Article (Academic Journal)

AN - SCOPUS:84988805362

SN - 0944-2669

VL - 55

JO - Calculus of Variable and Partial Differential Equations

JF - Calculus of Variable and Partial Differential Equations

IS - 5

M1 - 119

ER -

Stability of point defects of degree ±12 in a two-dimensional nematic liquid crystal model

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Dr Valeriy Slastikov

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Stability of point defects of degree ±12 in a two-dimensional nematic liquid crystal model

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Dr Valeriy Slastikov

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