Skip to main content Accessibility help
×
Home

Uniqueness of stable Meissner state solutions of the Chern-Simons-Higgs energy

  • Daniel Spirn (a1) and Xiaodong Yan (a2)

Abstract

For external magnetic field h ex –α , we prove that a Meissner state solution for the Chern-Simons-Higgs functional exists. Furthermore, if the solution is stable among all vortexless solutions, then it is unique.

Copyright

References

Hide All
[1] Almeida, L. and Bethuel, F., Topological methods for the Ginzburg-Landau equations. J. Math. Pures. Appl. 77 (1998) 149.
[2] Bethuel, F., Brezis, H. and Hélein, F., Asymptotics for the minimization of a Ginzburg-Landau functional. Cal. Var. Partial Differ. Equ. 1 (1993) 123148.
[3] Bonnet, A., Chapman, S.J. and Monneau, R., Convergence of Meissner minimizers of the Ginzburg-Landau energy of superconductivity as κ → +∞. SIAM J. Math. Anal. 31 (2000) 13741395.
[4] Choe, K. and Nam, H.-S., Existence and uniqueness of topological multivortex solutions of the self-dual Chern-Simons CP(1) model. Nonlinear Anal. 66 (2007) 27942813.
[5] Kurzke, M. and Spirn, D., Gamma limit of the nonself-dual Chern-Simons-Higgs energy. J. Funct. Anal. 244 (2008) 535588.
[6] Kurzke, M. and Spirn, D., Scaling limits of the Chern-Simons-Higgs energy. Commun. Contemp. Math. 10 (2008) 116.
[7] F. Pacard and T. Rivière, Linear and nonlinear aspects of vortices. The Ginzburg-Landau model. Progress in Nonlinear Differential Equations and their Applications 39. Birkhäuser Boston, Inc., Boston, MA, USA (2000).
[8] E. Sandier and S. Serfaty, Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field. Ann. Inst. H. Poincaré, Anal. Non Linéaire 17 (2000) 119–145.
[9] Serfaty, S., Stable configurations in superconductivity: Uniqueness, mulitplicity, and vortex-nucleation. Arch. Rational Mech. Anal. 149 (1999) 329365.
[10] D. Spirn and X. Yan, Minimizers near the first critical field for the nonself-dual Chern-Simons-Higgs energy. Calc. Var. Partial Differ. Equ. (to appear).
[11] Tarantello, G., Uniqueness of selfdual periodic Chern-Simons vortices of topological-type. Calc. Var. Partial Differ. Equ. 29 (2007) 191217.
[12] Ye, D. and Zhou, F., Uniqueness of solutions of the Ginzburg-Landau problem. Nonlinear Anal. 26 (1996) 603612.

Keywords

Uniqueness of stable Meissner state solutions of the Chern-Simons-Higgs energy

  • Daniel Spirn (a1) and Xiaodong Yan (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed