Dynamique des tourbillons de vorticité pour l’équation de Ginzburg-Landau parabolique

Fabrice Bethuel; Giandomenico Orlandi; Didier Smets

Séminaire Équations aux dérivées partielles (2006-2007)

  • Volume: 342, Issue: 11, page 1-16

How to cite

top

Bethuel, Fabrice, Orlandi, Giandomenico, and Smets, Didier. "Dynamique des tourbillons de vorticité pour l’équation de Ginzburg-Landau parabolique." Séminaire Équations aux dérivées partielles 342.11 (2006-2007): 1-16. <http://eudml.org/doc/11153>.

@article{Bethuel2006-2007,
author = {Bethuel, Fabrice, Orlandi, Giandomenico, Smets, Didier},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {complex parabolic Ginzburg-Landau equation; Kirchhoff-Onsager functional; vortex collisions},
language = {fre},
number = {11},
pages = {1-16},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Dynamique des tourbillons de vorticité pour l’équation de Ginzburg-Landau parabolique},
url = {http://eudml.org/doc/11153},
volume = {342},
year = {2006-2007},
}

TY - JOUR
AU - Bethuel, Fabrice
AU - Orlandi, Giandomenico
AU - Smets, Didier
TI - Dynamique des tourbillons de vorticité pour l’équation de Ginzburg-Landau parabolique
JO - Séminaire Équations aux dérivées partielles
PY - 2006-2007
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 342
IS - 11
SP - 1
EP - 16
LA - fre
KW - complex parabolic Ginzburg-Landau equation; Kirchhoff-Onsager functional; vortex collisions
UR - http://eudml.org/doc/11153
ER -

References

top
  1. L. Almeida, F. Bethuel, Topological methods for the Ginzburg-Landau equations, J. Math. Pures Appl. 77 (1998), 1–49. Zbl0904.35023MR1617594
  2. F. Bethuel, G. Orlandi, Ginzburg-Landau functionals, phase transitions and vorticity. In Noncompact problems at the intersection of geometry, analysis, and topology, 35–47, Contemp. Math. 350, Amer. Math. Soc., (2004). Zbl1073.35085MR2082389
  3. H. Brezis, J.M. Coron, H. Lieb, Harmonic maps with defects, Comm. Math. Phys.107 (1986), 649–705. Zbl0608.58016MR868739
  4. F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau vortices, Birkhäuser, Boston, (1994). Zbl0802.35142MR1269538
  5. F. Bethuel, G. Orlandi and D. Smets, Collisions and phase-vortex interaction in dissipative Ginzburg-Landau dynamics, Duke Math. J. 130 (2005), 523-614. Zbl1087.35008MR2184569
  6. F. Bethuel, G. Orlandi and D. Smets, Quantization and motion law for Ginzburg-Landau vortices, Arch. Rational Mech. Anal., 183 (2007), 315–370 Zbl1105.76062MR2278409
  7. F. Bethuel, G. Orlandi and D. Smets, Dynamics of multiple degree Ginzburg-Landau vortices, Comm. Math. Phys., à paraître. Zbl1135.35014
  8. F. Bethuel, G. Orlandi and D. Smets, On the Cauchy problem for phase and vortices in the parabolic Ginzburg-Landau equation, Proceedings Centre de recherche Mathématique de Montréal,à paraître. Zbl1144.35399
  9. M. Comte and P. Mironescu, Remarks on nonminimizing solutions of a Ginzburg-Landau type equation, Asymptotic Anal. 13 (1996), 199-215. Zbl0861.35023MR1413860
  10. W. E, Dynamics of vortices in Ginzburg-Landau theories with applications to superconductivity, Phys. D 77 (1994), 383-404. Zbl0814.34039MR1297726
  11. R.L. Jerrard and H.M. Soner, Dynamics of Ginzburg-Landau vortices, Arch. Rational Mech. Anal. 142 (1998), 99-125. Zbl0923.35167MR1629646
  12. F.H. Lin, Some dynamical properties of Ginzburg-Landau vortices, Comm. Pure Appl. Math. 49 (1996), 323-359. Zbl0853.35058MR1376654
  13. , S. Lojasiewicz, Une propiété topologique des sous-ensembles analytiques réels, Colloques internationaux du CNRS 117, Les équations aux dérivées partielles, 1963. Zbl0234.57007MR160856
  14. L. Peres and J. Rubinstein, Vortex dynamics in U ( 1 ) Ginzburg-Landau models, Phys. D 64 (1993), 299-309. Zbl0772.35069MR1214555
  15. P. Mironescu, Les minimiseurs locaux pour l’équation de Ginzburg-Landau sont à symétrie radiale, C. R. Acad. Sci. Paris Sér. I Math. 323 (1996), 593–598. Zbl0858.35038
  16. F. Pacard, T. Rivière, Linear and nonlinear aspects of vortices. The Ginzburg-Landau model. Progress in Nonlinear Differential Equations and their Applications 39. Birkhäuser Boston, (2000). Zbl0948.35003MR1763040
  17. E. Sandier and S. Serfaty, Gamma-convergence of gradient flows with applications to Ginzburg-Landau, Comm. Pure App. Math. 57 (2004), 1627-1672. Zbl1065.49011MR2082242
  18. S. Serfaty, Vortex Collision and Energy Dissipation Rates in the Ginzburg-Landau Heat Flow, preprint 2005. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.