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Stability of the melting hedgehog in the Landau-de Gennes theory of nematic liquid crystals

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arxiv 1404.1729 v1 pith:OBYUAYOB submitted 2014-04-07 math.AP cond-mat.softmath-phmath.MP

Radu Ignat , Luc Nguyen , Valeriy Slastikov , Arghir Zarnescu This is my paper · ORCID
classification math.APcond-mat.softmath-phmath.MP
keywords stabilityhedgehogmeltingnematiccrystalsdefectgennesliquid
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abstract

We investigate stability properties of the radially symmetric solution corresponding to the vortex defect (so called "melting hedgehog") in the framework of the Landau - de Gennes model of nematic liquid crystals. We prove local stability of the melting hedgehog under arbitrary $Q$-tensor valued perturbations in the temperature regime near the critical supercooling temperature. As a consequence of our method, we also rediscover the loss of stability of the vortex defect in the deep nematic regime.

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