Stable configurations in superconductivity: Uniqueness, multiplicity, and vortex-nucleation

Sylvia Serfaty

Research output: Contribution to journalArticlepeer-review


We find new stable solutions of the Ginzburg-Landau equation for high κ superconductors with exterior magnetic field hex. First, we prove the uniqueness of the Meissner-type solution. Then, we prove, in the case of a disc domain, the coexistence of branches of solutions with n vortices of degree one, for any n not too high and for a certain range of hex; and describe these branches. Finally, we give an estimate on the nucleation energy barrier, to pass continuously from a vortexless configuration to a configuration with a centered vortex.

Original languageEnglish (US)
Pages (from-to)329-365
Number of pages37
JournalArchive for Rational Mechanics and Analysis
Issue number4
StatePublished - Dec 18 1999

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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