GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY*

doi:10.1007/s10473-024-0507-2

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (5): 1747-1765.doi: 10.1007/s10473-024-0507-2

GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY^*

Xueli KE^1,2

1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China;
2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China

收稿日期:2023-01-08 修回日期:2024-04-30 出版日期:2024-10-25 发布日期:2024-10-22
作者简介:Xueli KE, E-mail,: kexueli123@126.com
基金资助:
National Natural Science Foundation of China (12371211, 12126359) and the postgraduate Scientific Research Innovation Project of Hunan Province (XDCX2022Y054, CX20220541).

GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY^*

Xueli KE^1,2

1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China;
2. School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China

Received:2023-01-08 Revised:2024-04-30 Online:2024-10-25 Published:2024-10-22
About author:Xueli KE, E-mail,: kexueli123@126.com
Supported by:
National Natural Science Foundation of China (12371211, 12126359) and the postgraduate Scientific Research Innovation Project of Hunan Province (XDCX2022Y054, CX20220541).

摘要/Abstract

摘要： We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations, with the initial data $(u_{0},B_{0})$ being located in the critical Besov space $\dot{B}_{p,1}^{-1+\frac{2}{p}}(\mathbb{R}^{2}) \,\, (1<p<2)$ and the initial density $\rho_{0}$ being close to a positive constant. By using weighted global estimates, maximal regularity estimates in the Lorentz space for the Stokes system, and the Lagrangian approach, we show that the 2-D MHD equations have a unique global solution.

关键词: inhomogeneous MHD equations, electrical conductivity, global unique solutions

Abstract: We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations, with the initial data $(u_{0},B_{0})$ being located in the critical Besov space $\dot{B}_{p,1}^{-1+\frac{2}{p}}(\mathbb{R}^{2}) \,\, (1<p<2)$ and the initial density $\rho_{0}$ being close to a positive constant. By using weighted global estimates, maximal regularity estimates in the Lorentz space for the Stokes system, and the Lagrangian approach, we show that the 2-D MHD equations have a unique global solution.

Key words: inhomogeneous MHD equations, electrical conductivity, global unique solutions

中图分类号:

35Q35

Xueli KE. GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY^*[J]. 数学物理学报(英文版), 2024, 44(5): 1747-1765.

Xueli KE. GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY^*[J]. Acta mathematica scientia,Series B, 2024, 44(5): 1747-1765.

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GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY^*

GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY^*

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