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 
@article{CRMATH_2013__351_13-14_533_0,
     author = {Radu Ignat and Luc Nguyen and Valeriy Slastikov and Arghir Zarnescu},
     title = {Stability of the vortex defect in the {Landau{\textendash}de} {Gennes} theory for nematic liquid crystals},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {533--537},
     publisher = {Elsevier},
     volume = {351},
     number = {13-14},
     year = {2013},
     doi = {10.1016/j.crma.2013.07.012},
     language = {en},
}
TY  - JOUR
AU  - Radu Ignat
AU  - Luc Nguyen
AU  - Valeriy Slastikov
AU  - Arghir Zarnescu
TI  - Stability of the vortex defect in the Landau–de Gennes theory for nematic liquid crystals
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 533
EP  - 537
VL  - 351
IS  - 13-14
PB  - Elsevier
DO  - 10.1016/j.crma.2013.07.012
LA  - en
ID  - CRMATH_2013__351_13-14_533_0
ER  - 
%0 Journal Article
%A Radu Ignat
%A Luc Nguyen
%A Valeriy Slastikov
%A Arghir Zarnescu
%T Stability of the vortex defect in the Landau–de Gennes theory for nematic liquid crystals
%J Comptes Rendus. Mathématique
%D 2013
%P 533-537
%V 351
%N 13-14
%I Elsevier
%R 10.1016/j.crma.2013.07.012
%G en
%F CRMATH_2013__351_13-14_533_0
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/

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

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

[3] E.C. Gartland; S. Mkaddem 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] S. Gustafson 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] 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

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

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

Cité par Sources :

Commentaires - Politique