Geodesic
Asymptotic analysis for the Ginzburg-Landau equations
Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 3, pp. 537-575.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Questo lavoro costituisce un survey sui problemi di limite asintotico per le soluzioni delle equazioni di Ginzburg-Landau in dimensione due. Vengono presentati essenzialmente i risultati di [BBH] e [BR] sulla formazione ed il comportamento asintotico dei vortici in un dominio bidimensionale nel caso fortemente repulsivo (large $K$ limit). 
@article{BUMI_1999_8_2B_3_a2,
     author = {Rivi\`ere, Tristan},
     title = {Asymptotic analysis for the {Ginzburg-Landau} equations},
     journal = {Bollettino della Unione matematica italiana},
     pages = {537--575},
     publisher = {mathdoc},
     volume = {Ser. 8, 2B},
     number = {3},
     year = {1999},
     zbl = {0939.35199},
     mrnumber = {1687389},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_1999_8_2B_3_a2/}
}
TY  - JOUR
AU  - Rivière, Tristan
TI  - Asymptotic analysis for the Ginzburg-Landau equations
JO  - Bollettino della Unione matematica italiana
PY  - 1999
SP  - 537
EP  - 575
VL  - 2B
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_1999_8_2B_3_a2/
LA  - en
ID  - BUMI_1999_8_2B_3_a2
ER  - 
%0 Journal Article
%A Rivière, Tristan
%T Asymptotic analysis for the Ginzburg-Landau equations
%J Bollettino della Unione matematica italiana
%D 1999
%P 537-575
%V 2B
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_1999_8_2B_3_a2/
%G en
%F BUMI_1999_8_2B_3_a2
Rivière, Tristan. Asymptotic analysis for the Ginzburg-Landau equations. Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 3, pp. 537-575. http://geodesic.mathdoc.fr/item/BUMI_1999_8_2B_3_a2/

[1] L. Almeida - F. Bethuel , Multiplicity results for the Ginzburg-Landau equation in presence of symmetries, Houston J. Math., 23 (1997), 733-764. | MR | Zbl

[2] L. Almeida - F. Bethuel , Topological Methods for the Ginzburg-Landau Equations, J. Math. Pures Appl., 77 (1998), 1-49. | MR | Zbl

[3] F. Bethuel - H. Brezis - F. Hélein , Asymptotics for the minimization of a Ginzburg-Landau functional, Calculus of variations and PDE 1 (1993), 123-148. | MR | Zbl

[4] F. Bethuel - H. Brezis - F. Hélein , Ginzburg-Landau vortices, Birkhaüser (1994). | MR | Zbl

[5] F. Bethuel - T. Rivière , Vortices for a variational problem related to supraconductivity, Ann. Inst. Henri Poincaré (analyse non linéaire), 12, 3 (1995), 243-303. | fulltext mini-dml | MR | Zbl

[6] F. Bethuel - T. Rivière , Vorticité dans les modèles de Ginzburg-Landau pour la supraconductivité, Ecole Polytechnique, Séminaire EDP XVI (1994). | fulltext mini-dml | MR | Zbl

[7] A. Jaffe - C. Taubes , Vortices and Monopoles, Birkhäuser (1980). | MR | Zbl

[8] R. Jerrard - M. Soner , Dynamics of Ginzburg-Landau Vortices, to appear in Arch. Rat. Mech. Anal. | Zbl

[9] F. H. Lin , Some Dynamical properties of Ginzburg-Landau Vortices, Comm. Pure and App. Math (1996), 323-359. A remark on the previous paper..., Comm. Pure and App. Math. (1996), 361-364. | MR | Zbl

[10] F. H. Lin , Complex Ginzburg-Landau Equations and Dynamics of Vortices, Filaments and Codimension 2 Submanifolds, preprint (1997). | MR | Zbl

[11] F. H. Lin - T. C. Lin , Minimax solutions of the Ginzburg-Landau equations, preprint (1996). | Zbl

[12] F. H. Lin - T. Rivière , Complex Ginzburg-Landau Equations in High Dimensions and Codimension two Area Minimizing Currents, to appear. | Zbl

[13] F. Pacard - T. Rivière , Construction of Ginzburg-Landau solutions having regular zero-set for large coupling constant, preprint CMLA ENS-Cachan (1998).

[14] F. Pacard - T. Rivière , A uniqueness result for the minimizers of the Ginzburg-Landau Functional, preprint CMLA ENS-Cachan (1998).

[15] T. Rivière , Line vortices in the $U(1)$-Higgs Model, C.O.C.V., 1 (1996), 77-167. | fulltext mini-dml | MR | Zbl

[16] D. Saint-James - G. Sarma - E. J. Thomas , Type II Superconductivity, Pergamon Press (1969).

[17] S. Serfaty , Local minimizers for the Ginzburg-Landau energy near Critical Magnetic Field, preprint Orsay (1997). | Zbl

[18] M. Struwe , On the asymptotic behavior of minimizers of the Ginzburg-Landau model in 2-dimensions, J. Diff. Int. Equations, 7 (1994), 1613-1624 and Erratum in J. Diff. Int. | MR | Zbl