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A Stability Problem for the 3D Magnetohydrodynamic Equations Near Equilibrium

Authors
  • Ke, Xueli1
  • Yuan, Baoquan1
  • Xiao, Yaomin1
  • 1 Henan Polytechnic University, Henan, Jiaozuo, 454000, China , Jiaozuo (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jun 01, 2021
Volume
41
Issue
4
Pages
1107–1118
Identifiers
DOI: 10.1007/s10473-021-0405-9
Source
Springer Nature
Keywords
License
Yellow

Abstract

This paper is concerned with a stability problem on perturbations near a physically important steady state solution of the 3D MHD system. We obtain three major results. The first assesses the existence of global solutions with small initial data. Second, we derive the temporal decay estimate of the solution in the L2-norm, where to prove the result, we need to overcome the difficulty caused by the presence of linear terms from perturbation. Finally, the decay rate in L2 space for higher order derivatives of the solution is established.

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