A rigorous derivation of a free-boundary problem arising in superconductivity

Étienne Sandier, Sylvia Serfaty

Research output: Contribution to journalArticle

Abstract

We study the Ginzburg-Landau energy of superconductors submitted to a possibly non-uniform magnetic field, in the limit of a large Ginzburg-Landau parameter κ . We prove that the induced magnetic fields associated to minimizers of the energy-functional converge as κ→+∞ to the solution of a free-boundary problem. This free-boundary problem has a nontrivial solution only when the applied magnetic field is of the order of the "first critical field", i.e. of the order of logκ . In other cases, our results are contained in those we had previously obtained [15, 16, 14]. We also derive a convergence result for the density of vortices.

Original languageEnglish (US)
Pages (from-to)561-592
Number of pages32
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume33
Issue number4
StatePublished - May 2000

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Superconductivity
Free Boundary Problem
Ginzburg-Landau
Magnetic Field
Superconductor
Energy Functional
Nontrivial Solution
Minimizer
Convergence Results
Vortex
Converge
Energy

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A rigorous derivation of a free-boundary problem arising in superconductivity. / Sandier, Étienne; Serfaty, Sylvia.

In: Annales Scientifiques de l'Ecole Normale Superieure, Vol. 33, No. 4, 05.2000, p. 561-592.

Research output: Contribution to journalArticle

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