Weak solutions to the Ginzburg-Landau model in superconductivity with the temporal gauge

Jishan Fan, Tohru Ozawa

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We first prove the uniqueness of weak solutions (ψ, A) to the 3-D Ginzburg-Landau system in superconductivity with the temporal gauge if(ψ, A)W :={(ψ, Aψ∈ L2(0, T; L∞), which is a critical space for some positive constant T. We also prove the global existence of solutions for the Ginzburg-Landau system with magnetic diffusivity μ>f 0 or μ=0. Finally, we prove the uniform bounds with respect to μ of strong solutions in space dimensions d=2. Consequently, the existence of the limit as μ→0 can be established.

Original languageEnglish
Pages (from-to)2029-2038
Number of pages10
JournalApplicable Analysis
Volume95
Issue number9
DOIs
Publication statusPublished - 2016 Sep 1

Keywords

  • Uniqueness
  • superconductivity
  • temporal gauge
  • weak solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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