On an Lp approach to the stationary and nonstationary problems of the Ginzburg-Landau-Maxwell equations

Takahiro Akiyama, Yoshihiro Shibata

    研究成果: Article

    1 引用 (Scopus)

    抄録

    In this paper, we study a stationary and a nonstationary problem of the Ginzburg-Landau-Maxwell equations with Coulomb gauge in the Lp framework. First we prove a unique existence of stationary solution near the constant state with a small external magnetic field. Moreover, we prove a globally in time existence of solutions to the time dependent Ginzburg-Landau-Maxwell equations with small initial data and external magnetic field, and we show its convergence to the corresponding stationary solution when time tends to infinity. The key of our approach is to use various Lp-Lq estimates of the analytic semigroup generated by the linearized problem. Especially our initial data belong to L3 without any additional regularity.

    元の言語English
    ページ(範囲)1-23
    ページ数23
    ジャーナルJournal of Differential Equations
    243
    発行部数1
    DOI
    出版物ステータスPublished - 2007 12 1

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    Ginzburg-Landau
    Maxwell equations
    Stationary Solutions
    Maxwell's equations
    External Field
    Magnetic Field
    Magnetic fields
    Lp Estimates
    Analytic Semigroup
    Gages
    Existence of Solutions
    Gauge
    Regularity
    Infinity
    Tend
    Framework

    ASJC Scopus subject areas

    • Analysis

    これを引用

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