数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (6): 1551-1567.doi: 10.1007/s10473-019-0607-6

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WELL-POSEDNESS AND STABILITY FOR THE GENERALIZED INCOMPRESSIBLE MAGNETO-HYDRODYNAMIC EQUATIONS IN CRITICAL FOURIER-BESOV-MORREY SPACES

Azzeddine EL BARAKA, Mohamed TOUMLILIN   

  1. FST FES, Laboratory AAFA, Department of Mathematics, University Sidi Mohamed Ben Abdellah, B. P 2202 Route Immouzer Fes 30000, Morocco
  • 收稿日期:2018-07-31 修回日期:2019-05-09 出版日期:2019-12-25 发布日期:2019-12-30
  • 通讯作者: Mohamed TOUMLILIN,E-mail:mohamed.toumlilin@usmba.ac.ma E-mail:mohamed.toumlilin@usmba.ac.ma
  • 作者简介:Azzeddine EL BARAKA,E-mail:azzeddine.elbaraka@usmba.ac.ma

WELL-POSEDNESS AND STABILITY FOR THE GENERALIZED INCOMPRESSIBLE MAGNETO-HYDRODYNAMIC EQUATIONS IN CRITICAL FOURIER-BESOV-MORREY SPACES

Azzeddine EL BARAKA, Mohamed TOUMLILIN   

  1. FST FES, Laboratory AAFA, Department of Mathematics, University Sidi Mohamed Ben Abdellah, B. P 2202 Route Immouzer Fes 30000, Morocco
  • Received:2018-07-31 Revised:2019-05-09 Online:2019-12-25 Published:2019-12-30
  • Contact: Mohamed TOUMLILIN,E-mail:mohamed.toumlilin@usmba.ac.ma E-mail:mohamed.toumlilin@usmba.ac.ma

摘要: This paper concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic (GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory, we get local well-posedness results of the GMHD equations with large initial data (u0, b0) belonging to the critical Fourier-Besov-Morrey spaces FṄp,λ,q1-2α+ 3/p'+λ/p (R3). Moreover, stability of global solutions is also discussed.

关键词: magneto-hydrodynamic, Fourier-Besov-Morrey space, stability

Abstract: This paper concerns the Cauchy problem of the 3D generalized incompressible magneto-hydrodynamic (GMHD) equations. By using the Fourier localization argument and the Littlewood-Paley theory, we get local well-posedness results of the GMHD equations with large initial data (u0, b0) belonging to the critical Fourier-Besov-Morrey spaces FṄp,λ,q1-2α+ 3/p'+λ/p (R3). Moreover, stability of global solutions is also discussed.

Key words: magneto-hydrodynamic, Fourier-Besov-Morrey space, stability

中图分类号: 

  • 35Q35