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Comptes Rendus Mathématique
Volume 351, n° 13-14
pages 533-537 (juillet 2013)
Doi : 10.1016/j.crma.2013.07.012
Received : 9 July 2013 ;  accepted : 11 July 2013
Stability of the vortex defect in the Landau–de Gennes theory for nematic liquid crystals
Stabilité du défaut vortex dans la théorie Landau–de Gennes pour les cristaux liquides
 

Radu Ignat a , Luc Nguyen b , Valeriy Slastikov c , Arghir Zarnescu d
a Laboratoire de mathématiques, Université ParisSud (Paris 11), bât. 425, 91405 Orsay cedex, France 
b Mathematics Department, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA 
c School of Mathematics, University of Bristol, Bristol, BS8 1TW, United Kingdom 
d University of Sussex, Department of Mathematics, Pevensey 2, Falmer, BN1 9QH, United Kingdom 

Abstract

We analyze the radially symmetric solution corresponding to the vortex defect (the so-called melting hedgehog ) in the Landau–de Gennes theory for nematic liquid crystals. We prove the existence, uniqueness and stability results of the melting hedgehog.

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Résumé

Nous étudions la solution à symétrie radiale associée au défaut de type vortex dans la théorie de Landau–de Gennes pour les cristaux liquides. Nous montrons des résultats dʼexistence, dʼunicité et de stabilité de cette solution.

The full text of this article is available in PDF format.
1  Recently, X. Lamy [[7]] showed the uniqueness and monotonicity of the energy-minimizing solution of Eq. ((1.4)) for the particular case of   given by ((1.5)) and on bounded domains by using a different technique.
2  The standard Hardy inequality in  :   for every  .
3  For instance, taking n large enough and defining   by   on  ,   on   and   elsewhere, we can choose   to be a smooth (compactly supported) approximation of ψ .


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