Geodesic
Instability of point defects in a two-dimensional nematic liquid crystal model
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 1131-1152

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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 3×3 matrices. These critical points play the role of topological point defects carrying a degree k2 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|≥2.

DOI : 10.1016/j.anihpc.2015.03.007
Keywords: Nonlinear elliptic PDE system, Singular ODE system, Stability, Vortex, Liquid crystal defects 
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     title = {Instability of point defects in a two-dimensional nematic liquid crystal model},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1131--1152},
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Ignat, Radu; Nguyen, Luc; Slastikov, Valeriy; Zarnescu, Arghir. Instability of point defects in a two-dimensional nematic liquid crystal model. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 1131-1152. doi: 10.1016/j.anihpc.2015.03.007

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