Comptes Rendus
no. 13-14
Partial Differential Equations/Calculus of Variations
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]

Présenté par : John Ball

Radu Ignat1 ; Luc Nguyen2 ; Valeriy Slastikov3 ; Arghir Zarnescu4
1 Laboratoire de mathématiques, Université ParisSud (Paris 11), bât. 425, 91405 Orsay cedex, France
2 Mathematics Department, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA
3 School of Mathematics, University of Bristol, Bristol, BS8 1TW, United Kingdom
4 University of Sussex, Department of Mathematics, Pevensey 2, Falmer, BN1 9QH, United Kingdom
Comptes Rendus. Mathématique, Volume 351 (2013) no. 13-14, pp. 533-537.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.07.012

Radu Ignat 1 ; Luc Nguyen 2 ; Valeriy Slastikov 3 ; Arghir Zarnescu 4

1 Laboratoire de mathématiques, Université ParisSud (Paris 11), bât. 425, 91405 Orsay cedex, France
2 Mathematics Department, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA
3 School of Mathematics, University of Bristol, Bristol, BS8 1TW, United Kingdom
4 University of Sussex, Department of Mathematics, Pevensey 2, Falmer, BN1 9QH, United Kingdom 
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     title = {Stability of the vortex defect in the {Landau{\textendash}de} {Gennes} theory for nematic liquid crystals},
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Radu Ignat; Luc Nguyen; Valeriy Slastikov; Arghir Zarnescu. Stability of the vortex defect in the Landau–de Gennes theory for nematic liquid crystals. Comptes Rendus. Mathématique, Volume 351 (2013) no. 13-14, pp. 533-537. doi : 10.1016/j.crma.2013.07.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.07.012/

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[5] R. Ignat, L. Nguyen, V. Slastikov, A. Zarnescu, Uniqueness result for an ODE related to a generalized Ginzburg–Landau model for liquid crystals, in preparation.

[6] R. Ignat, L. Nguyen, V. Slastikov, A. Zarnescu, On stability of the radially symmetric solution in a Landau–de Gennes model for liquid crystals, in preparation.

[7] X. Lamy Some properties of the nematic radial hedgehog in the Landau–de Gennes theory, J. Math. Anal. Appl., Volume 397 (2013), pp. 586-594

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