Vortex collisions and energy-dissipation rates in the Ginzburg-Landau heat flow Part II: The dynamics

Journal of the European Mathematical Society

Volumn 9, Issue 3, 2007, Pages 383-426

  Serfaty, Sylvia ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Ginzburg landau equation; Ginzburg landau vortices; Vortex collisions; Vortex dynamics

Indexed keywords

EID: 34250327168     PISSN: 14359855     EISSN: None     Source Type: Journal    
DOI: 10.4171/JEMS/84     Document Type: Article

References (23)

1. Alberti, G.: A variational convergence result for Ginzburg-Landau functionals in any dimension. Boll. Unione Mat. Ital. Sez. B 4, 289-310 (2001) (in Italian) Zbl 1036.49021 MR 1831990
2. Almeida, L., Bethuel, F.: Topological methods for the Ginzburg-Landau equations. J. Math. Pures Appl. (9) 77, 1-49 (1998) Zbl 0904.35023 MR 1617594
3. Bauman, P., Chen, C. N., Phillips, D., Sternberg, P.: Vortex annihilation in nonlinear heat flow for Ginzburg-Landau systems, European J. Appl. Math. 6, 115-126 (1995) Zbl 0845.35042 MR 1331494
4. Bethuel, F., Brezis, H., Hélein, F.: Ginzburg-Landau Vortices. Birkhäuser (1994) Zbl 0802.35142 MR 1269538
5. Bethuel, F., Orlandi, G., Smets, D.: Collisions and phase-vortex interactions in dissipative Ginzburg-Landau dynamics. Duke Math. J. 130, 523-614 (2005) Zbl 1087.35008 MR 2184569
6. Bethuel, F., Orlandi, G., Smets, D.: Quantization and motion law for Ginzburg-Landau vortices. Arch. Ration. Mech. Anal. 183, 315-370 (2007) Zbl 1105.76062 MR 2278409
7. Bethuel, F., Orlandi, G., Smets, D.: Dynamics of multiple degree Ginzburg-Landau vortices. Preprint (2006)
8. Jerrard, R. L., Soner, H. M.: Dynamics of Ginzburg-Landau vortices. Arch. Ration. Mech. Anal. 142, 99-125 (1998) Zbl 0923.35167 MR 1629646
9. Jerrard, R. L., Soner, H. M.: The Jacobian and the Ginzburg-Landau functional. Cale. Var. Partial Differential Equations 14, 151-191 (2002) Zbl 1034.35025 MR 1890398
10. Lin, F. H.: Some dynamical properties of Ginzburg-Landau vortices. Comm. Pure Appl. Math. 49, 323-359 (1996) Zbl 0853.35058 MR 1376654
11. Mironescu, P.: Les minimiseurs locaux pour l'équation de Ginzburg-Landau sont à symétrie radiale. C. R. Acad. Sci. Paris Sér. I Math. 323, 593-598 (1996) Zbl 0858.35038 MR 1411048
12. Rubinstein, J., Sternberg, P.: On the slow motion of vortices in the Ginzburg-Landau heat-flow. SIAM J. Appl. Math. 26, 1452-1466 (1995) Zbl 0838.35102 MR 1356453
13. Ovchinnikov, Y. N., Sigal, I. M.: Symmetry-breaking solutions to the Ginzburg-Landau equation. J. Exp. Theor. Phys. 99, 1090-1107 (2004) MR 2108700
14. Sandier, E.: Lower bounds for the energy of unit vector fields and applications. J. Funct. Anal. 152 (1998), 379-403; Erratum, ibid. 171, 233 (2000) Zbl 0908.58004 MR 1607928
15. 2. Proc. Roy. Soc. Edinburgh Sect. A 128, 349-358 (1998) Zbl 0905.35018 MR 1621347
16. Sandier, E., Serfaty, S.: A product estimate for Ginzburg-Landau and corollaries. J. Funct. Anal. 211, 219-244 (2004) Zbl 1063.35144 MR 2054623
17. Sandier, E., Serfaty, S.: Gamma-convergence of gradient flows and application to Ginzburg-Landau. Comm. Pure Appl. Math. 57, 1627-1672 (2004) Zbl 1065.49011 MR 2082242
18. Sandier, E., Serfaty, S.: A rigorous derivation of a free-boundary problem arising in superconductivity. Ann. Sci. École Norm. Sup. 33, 561-592 (2000) Zbl pre01702168 MR 1832824
19. Sandier, E., Serfaty, S.: Vortices in the Magnetic Ginzburg-Landau Model. Progr. Nonlinear Partial Differential Equations 70, Birkhäuser (2007) Zbl pre05116147 MR 2279839
20. Serfaty, S.: Vortex collisions and energy-dissipation rates in the Ginzburg-Landau heat flow, Part I: Study of the perturbed Ginzburg-Landau equation. J. Eur. Math. Soc. 9, 177-217 (2007)
21. Serfaty, S.: Stability in 2D Ginzburg-Landau passes to the limit. Indiana Univ. Math. J. 54, 199-222 (2005) Zbl pre02174725 MR 2126721
22. Soner, H. M.: Ginzburg-Landau equation and motion by mean curvature. I. Convergence, II. Development of the initial interface. J. Geom. Anal. 7, 437-491 (1997) Zbl 0935.35060 MR 1674799
23. Spirn, D.: Vortex dynamics for the full time-dependent Ginzburg-Landau equations. Comm. Pure Appl. Math. 55, 537-581 (2002) Zbl 1032.35163 MR 1880643