Instability of point defects in a two-dimensional nematic liquid crystal model

Radu Ignat; Luc Nguyen; Valeriy Slastikov; Arghir Zarnescu

doi:10.1016/j.anihpc.2015.03.007

JournalsaihpcVol. 33, No. 4pp. 1131–1152

Instability of point defects in a two-dimensional nematic liquid crystal model

Radu Ignat
Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31062 Toulouse, France
Luc Nguyen
Mathematical Institute and St Edmund Hall, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom
Valeriy Slastikov
School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom
Arghir Zarnescu
University of Sussex, Department of Mathematics, Pevensey 2, Falmer, BN1 9QH, United Kingdom; Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 21 Calea Grivitei Street, 01702 Bucharest, Romania

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Abstract

We study a class of symmetric critical points in a variational 2D Landau–de Gennes model where the state of nematic liquid crystals is described by symmetric traceless $3 \times 3$ matrices. These critical points play the role of topological point defects carrying a degree $\frac{k}{2}$ for a nonzero integer k. We prove existence and study the qualitative behavior of these symmetric solutions. Our main result is the instability of critical points when $∣ k ∣ \geq 2$ .

Cite this article

Radu Ignat, Luc Nguyen, Valeriy Slastikov, Arghir Zarnescu, Instability of point defects in a two-dimensional nematic liquid crystal model. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 4, pp. 1131–1152

DOI 10.1016/J.ANIHPC.2015.03.007