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

Jishan Fan, Tohru Ozawa

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    Abstract

    We first prove the uniqueness of weak solutions (Formula presented.) to the 3-D Ginzburg-Landau system in superconductivity with the temporal gauge if (Formula presented.), which is a critical space for some positive constant (Formula presented.). We also prove the global existence of solutions for the Ginzburg-Landau system with magnetic diffusivity (Formula presented.) or (Formula presented.). Finally, we prove the uniform bounds with respect to (Formula presented.) of strong solutions in space dimensions (Formula presented.). Consequently, the existence of the limit as (Formula presented.) can be established.

    Original languageEnglish
    JournalApplicable Analysis
    DOIs
    Publication statusAccepted/In press - 2015 Sep 9

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    Keywords

    • superconductivity
    • temporal gauge
    • Uniqueness
    • weak solutions

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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