Partial Differential Equations/Calculus of Variations
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.

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.

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.

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DOI: 10.1016/j.crma.2013.07.012
Ignat, Radu 1; Nguyen, Luc 2; Slastikov, Valeriy 3; Zarnescu, Arghir 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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Ignat, Radu; Nguyen, Luc; Slastikov, Valeriy; Zarnescu, Arghir. 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. http://www.numdam.org/articles/10.1016/j.crma.2013.07.012/

[1] Ball, J.M.; Zarnescu, A. Orientability and energy minimization in liquid crystal models, Arch. Ration. Mech. Anal., Volume 202 (2011), pp. 493-535

[2] Bethuel, F.; Brezis, H.; Helein, F. Ginzburg–Landau Vortices, Birkhäuser Boston, 1994

[3] Gartland, E.C.; Mkaddem, S. Instability of radial hedgehog configurations in nematic liquid crystals under Landau–de Gennes free-energy models, Phys. Rev. E, Volume 59 (1999), pp. 563-567

[4] Gustafson, S. Symmetric solutions of the Ginzburg–Landau equations in all dimensions, Int. Math. Res. Not. IMRN, Volume 16 (1997), pp. 807-816

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

[8] Majumdar, A.; Zarnescu, A. Landau–de Gennes theory of nematic liquid crystals: the Oseen–Frank limit and beyond, Arch. Ration. Mech. Anal., Volume 196 (2010), pp. 227-280

[9] Millot, V.; Pisante, A. Symmetry of local minimizers for the three-dimensional Ginzburg–Landau functional, J. Eur. Math. Soc. (JEMS), Volume 12 (2010), pp. 1069-1096

[10] Mironescu, P. On the stability of radial solutions of the Ginzburg–Landau equation, J. Funct. Anal., Volume 130 (1995), pp. 334-344

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