A Stability Problem for the 3D Magnetohydrodynamic Equations Near Equilibrium

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...

Full description

Saved in:
Bibliographic Details
Published inActa mathematica scientia Vol. 41; no. 4; pp. 1107 - 1118
Main Authors Ke, Xueli, Yuan, Baoquan, Xiao, Yaomin
Format Journal Article
LanguageEnglish
Published Singapore Springer Singapore 01.07.2021
Subjects
Analysis
Mathematics
Mathematics and Statistics
decay rate
35B35
35Q35
35A01
Background magnetic field
MHD equations with perturbation
stability
Online AccessGet full text

Cover

More Information
Summary: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 L 2 -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 L 2 space for higher order derivatives of the solution is established.
ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-021-0405-9