Problèmes d’évolution liés à l’énergie de Ginzburg-Landau
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2002-2003), Talk no. 12, 15 p.
Smets, Didier 1

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 175 rue du Chevaleret,75013 Paris FRANCE
@article{SEDP_2002-2003____A12_0,
     author = {Smets, Didier},
     title = {Probl\`emes d{\textquoteright}\'evolution li\'es \`a l{\textquoteright}\'energie de {Ginzburg-Landau}},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:12},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2002-2003},
     zbl = {1092.35106},
     language = {fr},
     url = {http://archive.numdam.org/item/SEDP_2002-2003____A12_0/}
}
TY  - JOUR
AU  - Smets, Didier
TI  - Problèmes d’évolution liés à l’énergie de Ginzburg-Landau
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:12
PY  - 2002-2003
DA  - 2002-2003///
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://archive.numdam.org/item/SEDP_2002-2003____A12_0/
UR  - https://zbmath.org/?q=an%3A1092.35106
LA  - fr
ID  - SEDP_2002-2003____A12_0
ER  - 
%0 Journal Article
%A Smets, Didier
%T Problèmes d’évolution liés à l’énergie de Ginzburg-Landau
%J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
%Z talk:12
%D 2002-2003
%I Centre de mathématiques Laurent Schwartz, École polytechnique
%G fr
%F SEDP_2002-2003____A12_0
Smets, Didier. Problèmes d’évolution liés à l’énergie de Ginzburg-Landau. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2002-2003), Talk no. 12, 15 p. http://archive.numdam.org/item/SEDP_2002-2003____A12_0/

[1] G. Alberti, S. Baldo et G. Orlandi, Variational convergence for functionals of Ginzburg-Landau type, préprint 2002. | MR

[2] A. Ambrosetti et M. Struwe, Existence of steady vortex rings in an ideal fluid, Arch. Rational Mech. Anal. 108 (1989), 97-109. | MR | Zbl

[3] L. Ambrosio and M. Soner, A measure theoretic approach to higher codimension mean curvature flow, Ann. Sc. Norm. Sup. Pisa, Cl. Sci. 25 (1997), 27-49. | Numdam | MR | Zbl

[4] F. Bethuel, H. Brezis et F. Hélein, Ginzburg-Landau vortices, Birkhäuser, Boston, 1994. | MR | Zbl

[5] F. Bethuel, H. Brezis et G. Orlandi, Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions, J. Funct. Anal. 186 (2001), 432-520. Erratum 188 (2002), 548-549. | MR | Zbl

[6] F. Bethuel, G. Orlandi et D. Smets, Vortex rings for the Gross-Pitaevskii equation, Jour. Eur. Math. Soc., à paraître. | MR | Zbl

[7] F. Bethuel, G. Orlandi et D. Smets, Convergence of the parabolic Ginzburg-Landau equation to motion by mean curvature, préprint. | MR

[8] K. Brakke, The motion of a surface by its mean curvature, Princeton University Press, 1978. | MR | Zbl

[9] L. E. Fraenkel et M. S. Berger, A global theory of steady vortex rings in an ideal fluid, Acta Math. 132 (1974), 13-51. | MR | Zbl

[10] H. Helmholtz, Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelwegungen entsprechen, J. Reine Angew. Math 55 (1858), 25-55. | Zbl

[11] G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geom. 20 (1984), 237-266. | MR | Zbl

[12] G. Huisken, Asymptotic behavior for singularities of the mean curvature flow, J. Differential Geom. 31 (1990), 285-299. | MR | Zbl

[13] T. Ilmanen, Convergence of the Allen-Cahn equation to Brakke’s motion by mean curvature, J. Differential Geom. 38 (1993), 417-461. | Zbl

[14] T. Ilmanen, Elliptic regularization and partial regularity for motion by mean curvature, Mem. Amer. Math. Soc. 108 (1994), no. 520. | MR | Zbl

[15] F.H. Lin et T. Rivière, Complex Ginzburg-Landau equation in high dimension and codimension 2 area minimizing currents, J. Eur. Math. Soc. 1 (1999), 237-311. Erratum, Ibid. | MR | Zbl

[16] F.H. Lin et T. Rivière, A quantization property for static Ginzburg-Landau vortices, Comm. Pure Appl. Math. 54 (2001), 206-228. | MR | Zbl

[17] F.H. Lin et T. Rivière, A quantization property for moving line vortices, Comm. Pure Appl. Math. 54 (2001), 826-850. | MR | Zbl

[18] R.L. Jerrard, Vortex filament dynamics for Gross-Pitaevsky like equations, I, prépublication.

[19] D.W. Moore et D.I. Pullin, On steady compressible flows with compact vorticity ; the compressible Hill’s spherical vortex, J. Fluid Mech. 374 (1998), 285-303. | Zbl

[20] T. Rivière, Line vortices in the U(1) Higgs model, ESAIM, C.O.C.V. 1 (1996), 77-167. | Numdam | MR | Zbl

[21] R. Schoen et K. Uhlenbeck, A regularity theory for harmonic maps, J. Differential Geom. 17 (1982), 307-335. | MR | Zbl

[22] E. Sandier et Sylvia Serfaty, High Kappa Limit of the Ginzburg-Landau Equations of Superconductivity, Duke Math. Journal, à paraître.

[23] E. Sandier et Sylvia Serfaty, The decrease of bulk superconductivity near the second critical field in the Ginzburg-Landau model, prépublication.

[24] M. Struwe, On the evolution of harmonic maps in higher dimensions, J. Diff. Geom. 28 (1988), 485-502. | MR | Zbl

[25] C. Wang, On moving Ginzburg-Landau filament vortices, Max-Planck-Institut Leipzig, préprint.