The decrease of bulk-superconductivity close to the second critical field in the ginzburg-landau model

Etienne Sandier, Sylvia Serfaty

Research output: Contribution to journalArticle


We study solutions of the Ginzburg-Landau equations describing superconductors in a magnetic field, just below the "second critical field" Hc2. We thus bridge the gap between the situations described in [E. Sandier and S. Serfaty, Rev. Math. Phys., 12 (2000), pp. 1219-1257] and [X. B. Pan, Comm. Math. Phys., 228 (2002), pp. 327-370]. We prove estimates on the energy, among them one by an algebraic trick inspired by the Bogomoln'yi trick for self-duality. We thus show how, for energy-minimizers, superconductivity decreases in average in the bulk of the sample when the applied field increases to Hc2.

Original languageEnglish (US)
Pages (from-to)939-956
Number of pages18
JournalSIAM Journal on Mathematical Analysis
Issue number4
StatePublished - Jan 1 2003



  • Asymptotic analysis
  • Phase transitions
  • Second critical field
  • Superconductivity

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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