Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T19:23:29.095Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  21 October 2008

Daniel Spirn  and
Xiaodong Yan
Daniel Spirn
Affiliation:
University of Minnesota, USA. spirn@math.umn.edu
Xiaodong Yan
Affiliation:
University of Connecticut, USA. xiaodong@math.uconn.edu
Get access

Abstract

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

Keywords

Chern-Simons-Higgs theorysuperconductivityuniquenessMeissner solution
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 1 , January 2010 , pp. 23 - 36
Copyright
© EDP Sciences, SMAI, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Almeida, L. and Bethuel, F., Topological methods for the Ginzburg-Landau equations. J. Math. Pures. Appl. 77 (1998) 1–49. CrossRef
Bethuel, F., Brezis, H. and Hélein, F., Asymptotics for the minimization of a Ginzburg-Landau functional. Cal. Var. Partial Differ. Equ. 1 (1993) 123–148. CrossRef
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) 1374–1395. CrossRef
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) 2794–2813. CrossRef
Kurzke, M. and Spirn, D., Gamma limit of the nonself-dual Chern-Simons-Higgs energy. J. Funct. Anal. 244 (2008) 535–588. CrossRef
Kurzke, M. and Spirn, D., Scaling limits of the Chern-Simons-Higgs energy. Commun. Contemp. Math. 10 (2008) 1–16. CrossRef
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).
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.
Serfaty, S., Stable configurations in superconductivity: Uniqueness, mulitplicity, and vortex-nucleation. Arch. Rational Mech. Anal. 149 (1999) 329–365. CrossRef
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).
Tarantello, G., Uniqueness of selfdual periodic Chern-Simons vortices of topological-type. Calc. Var. Partial Differ. Equ. 29 (2007) 191–217. CrossRef
Ye, D. and Zhou, F., Uniqueness of solutions of the Ginzburg-Landau problem. Nonlinear Anal. 26 (1996) 603–612. CrossRef