A STABILITY PROBLEM FOR THE 3D MAGNETOHYDRODYNAMIC EQUATIONS NEAR EQUILIBRIUM

doi:10.1007/s10473-021-0405-9

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (4): 1107-1118.doi: 10.1007/s10473-021-0405-9

A STABILITY PROBLEM FOR THE 3D MAGNETOHYDRODYNAMIC EQUATIONS NEAR EQUILIBRIUM

可雪丽, 原保全, 肖亚敏

School of Mathematics and Information Science, Henan Polytechnic University, Henan 454000, China

收稿日期:2020-01-05 修回日期:2020-08-20 出版日期:2021-08-25 发布日期:2021-09-01
通讯作者: Baoquan YUAN E-mail:bqyuan@hpu.edu.cn
作者简介:Xueli KE,E-mail:kexueli123@126.com; Baoquan YUAN, E-mail:bqyuan@hpu.edu.cn;Yaomin XIAO,E-mail:ymxiao106@163.com
基金资助:
The second author is supported by the National Natural Science Foundation of China (11471103).

A STABILITY PROBLEM FOR THE 3D MAGNETOHYDRODYNAMIC EQUATIONS NEAR EQUILIBRIUM

Xueli KE, Baoquan YUAN, Yaomin XIAO

School of Mathematics and Information Science, Henan Polytechnic University, Henan 454000, China

Received:2020-01-05 Revised:2020-08-20 Online:2021-08-25 Published:2021-09-01
Contact: Baoquan YUAN E-mail:bqyuan@hpu.edu.cn
Supported by:
The second author is supported by the National Natural Science Foundation of China (11471103).

摘要/Abstract

摘要： 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.

关键词: Background magnetic field, MHD equations with perturbation, stability, decay rate

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.

Key words: Background magnetic field, MHD equations with perturbation, stability, decay rate

中图分类号:

35Q35

可雪丽, 原保全, 肖亚敏. A STABILITY PROBLEM FOR THE 3D MAGNETOHYDRODYNAMIC EQUATIONS NEAR EQUILIBRIUM[J]. 数学物理学报(英文版), 2021, 41(4): 1107-1118.

Xueli KE, Baoquan YUAN, Yaomin XIAO. A STABILITY PROBLEM FOR THE 3D MAGNETOHYDRODYNAMIC EQUATIONS NEAR EQUILIBRIUM[J]. Acta mathematica scientia,Series B, 2021, 41(4): 1107-1118.

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A STABILITY PROBLEM FOR THE 3D MAGNETOHYDRODYNAMIC EQUATIONS NEAR EQUILIBRIUM

A STABILITY PROBLEM FOR THE 3D MAGNETOHYDRODYNAMIC EQUATIONS NEAR EQUILIBRIUM

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