Problèmes d’évolution liés à l’énergie de Ginzburg-Landau
Didier Smets[1]
- [1] Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 175 rue du Chevaleret,75013 Paris FRANCE
Séminaire Équations aux dérivées partielles (2002-2003)
- Volume: 2002-2003, page 1-15
Access Full Article
topHow to cite
topSmets, Didier. "Problèmes d’évolution liés à l’énergie de Ginzburg-Landau." Séminaire Équations aux dérivées partielles 2002-2003 (2002-2003): 1-15. <http://eudml.org/doc/11054>.
@article{Smets2002-2003,
affiliation = {Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 175 rue du Chevaleret,75013 Paris FRANCE},
author = {Smets, Didier},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {Ginzburg-Landau equation; vortex ring; Gross-Pitaevskii equation; Bose-Einstein condensates},
language = {fre},
pages = {1-15},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Problèmes d’évolution liés à l’énergie de Ginzburg-Landau},
url = {http://eudml.org/doc/11054},
volume = {2002-2003},
year = {2002-2003},
}
TY - JOUR
AU - Smets, Didier
TI - Problèmes d’évolution liés à l’énergie de Ginzburg-Landau
JO - Séminaire Équations aux dérivées partielles
PY - 2002-2003
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2002-2003
SP - 1
EP - 15
LA - fre
KW - Ginzburg-Landau equation; vortex ring; Gross-Pitaevskii equation; Bose-Einstein condensates
UR - http://eudml.org/doc/11054
ER -
References
top- G. Alberti, S. Baldo et G. Orlandi, Variational convergence for functionals of Ginzburg-Landau type, préprint 2002. Zbl1160.35013MR2177107
- A. Ambrosetti et M. Struwe, Existence of steady vortex rings in an ideal fluid, Arch. Rational Mech. Anal. 108 (1989), 97-109. Zbl0694.76012MR1011553
- 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. Zbl1043.35136MR1655508
- F. Bethuel, H. Brezis et F. Hélein, Ginzburg-Landau vortices, Birkhäuser, Boston, 1994. Zbl0802.35142MR1269538
- 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. Zbl1077.35047MR1864830
- F. Bethuel, G. Orlandi et D. Smets, Vortex rings for the Gross-Pitaevskii equation, Jour. Eur. Math. Soc., à paraître. Zbl1091.35085MR2041006
- F. Bethuel, G. Orlandi et D. Smets, Convergence of the parabolic Ginzburg-Landau equation to motion by mean curvature, préprint. Zbl1031.35026MR1988309
- K. Brakke, The motion of a surface by its mean curvature, Princeton University Press, 1978. Zbl0386.53047MR485012
- L. E. Fraenkel et M. S. Berger, A global theory of steady vortex rings in an ideal fluid, Acta Math. 132 (1974), 13-51. Zbl0282.76014MR422916
- H. Helmholtz, Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelwegungen entsprechen, J. Reine Angew. Math 55 (1858), 25-55.
- G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geom. 20 (1984), 237-266. Zbl0556.53001MR772132
- G. Huisken, Asymptotic behavior for singularities of the mean curvature flow, J. Differential Geom. 31 (1990), 285-299. Zbl0694.53005MR1030675
- T. Ilmanen, Convergence of the Allen-Cahn equation to Brakke’s motion by mean curvature, J. Differential Geom. 38 (1993), 417-461. Zbl0784.53035
- T. Ilmanen, Elliptic regularization and partial regularity for motion by mean curvature, Mem. Amer. Math. Soc. 108 (1994), no. 520. Zbl0798.35066MR1196160
- 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. Zbl0939.35056MR1714735
- F.H. Lin et T. Rivière, A quantization property for static Ginzburg-Landau vortices, Comm. Pure Appl. Math. 54 (2001), 206-228. Zbl1033.58013MR1794353
- F.H. Lin et T. Rivière, A quantization property for moving line vortices, Comm. Pure Appl. Math. 54 (2001), 826-850. Zbl1029.35127MR1823421
- R.L. Jerrard, Vortex filament dynamics for Gross-Pitaevsky like equations, I, prépublication. Zbl1170.35318
- 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. Zbl0936.76075
- T. Rivière, Line vortices in the Higgs model, ESAIM, C.O.C.V. 1 (1996), 77-167. Zbl0874.53019MR1394302
- R. Schoen et K. Uhlenbeck, A regularity theory for harmonic maps, J. Differential Geom. 17 (1982), 307-335. Zbl0521.58021MR664498
- E. Sandier et Sylvia Serfaty, High Kappa Limit of the Ginzburg-Landau Equations of Superconductivity, Duke Math. Journal, à paraître.
- E. Sandier et Sylvia Serfaty, The decrease of bulk superconductivity near the second critical field in the Ginzburg-Landau model, prépublication. Zbl1030.82015
- M. Struwe, On the evolution of harmonic maps in higher dimensions, J. Diff. Geom. 28 (1988), 485-502. Zbl0631.58004MR965226
- C. Wang, On moving Ginzburg-Landau filament vortices, Max-Planck-Institut Leipzig, préprint. Zbl1063.35081
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.