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

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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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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