A non-existence result for the Ginzburg–Landau equations

Ayman Kachmar; Mikael Persson

doi:10.1016/j.crma.2009.09.024

Partial Differential Equations

A non-existence result for the Ginzburg–Landau equations
[Un résultat de non-existence pour les équations de Ginzburg–Landau]

Présenté par : Haïm Brezis

Ayman Kachmar ¹ ; Mikael Persson ¹

¹ Aarhus University, Department of Mathematical Sciences, Ny Munkegade, DK-8000 Aarhus C, Denmark

Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1261-1264.

Résumé
Abstract

Nous considérons les équations de Ginzburg–Landau dans $R^{d}$ , $d = 2, 3$ . Nous exhibons une classe de champs magnétiques appliqués telle que les équations de Ginzburg–Landau n'admettent pas de solution d'énergie finie.

We consider the stationary Ginzburg–Landau equations in $R^{d}$ , $d = 2, 3$ . We exhibit a class of applied magnetic fields (including constant fields) such that the Ginzburg–Landau equations do not admit finite energy solutions.

Reçu le : 2009-07-15
Accepté le : 2009-09-23
Publié le : 2009-10-09

DOI : 10.1016/j.crma.2009.09.024

Affiliations des auteurs :

Ayman Kachmar ¹ ; Mikael Persson ¹

¹ Aarhus University, Department of Mathematical Sciences, Ny Munkegade, DK-8000 Aarhus C, Denmark

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     author = {Ayman Kachmar and Mikael Persson},
     title = {A non-existence result for the {Ginzburg{\textendash}Landau} equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1261--1264},
     publisher = {Elsevier},
     volume = {347},
     number = {21-22},
     year = {2009},
     doi = {10.1016/j.crma.2009.09.024},
     language = {en},
}

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Ayman Kachmar; Mikael Persson. A non-existence result for the Ginzburg–Landau equations. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1261-1264. doi : 10.1016/j.crma.2009.09.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.024/

Bibliographie
Cité par

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[2] H. Aydi; E. Sandier Vortex analysis of the periodic Ginzburg–Landau model, Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Volume 26 (2009) no. 4, pp. 1223-1236

[3] H.L. Cycon; R.G. Froese; W. Kirsh; B. Simon Schrödinger Operators, Springer-Verlag, Berlin, 1987

[4] M. Dutour Bifurcation vers l'état d'Abrikosov et diagramme des phases, Thèse, Orsay, 1999 http://xxx.lanl.gov/abs/math-ph/9912011 (available online at)

[5] S. Fournais, B. Helffer, Spectral Methods in Surface Superconductivity, Progress in Nonlinear Differential Equations and Their Applications, vol. 77, Birkhäuser, Basel, 2010, in press

[6] T. Giorgi; R. Smith Remarks on the existence of global minimizers for the Ginzburg–Landau energy functional, Nonlinear Anal., Volume 53 (2003) no. 2, pp. 147-155

[7] Y. Yang Existence regularity and asymptotic behavior of the solutions of the Ginzburg–Landau equations on $R^{3}$ , Comm. Math. Phys., Volume 123 (1989), pp. 147-161

[8] Y. Yang The existence of Ginzburg–Landau solutions on the plane by a direct variational method, Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Volume 11 (1994) no. 5, pp. 517-536

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