GLOBAL STRONG SOLUTIONS TO THE PLANAR COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH DEGENERATE HEAT-CONDUCTIVITY IN THE HALF-LINE

doi:10.1007/s10473-026-0112-7

数学物理学报(英文版) ›› 2026, Vol. 46 ›› Issue (1): 189-208.doi: 10.1007/s10473-026-0112-7

GLOBAL STRONG SOLUTIONS TO THE PLANAR COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH DEGENERATE HEAT-CONDUCTIVITY IN THE HALF-LINE

Mengdi TONG¹, Xue Wang², Rong ZHANG^3,*

1. School of Mathematics and Computer Sciences, Nanchang University, Nanchang 330031, China;
2. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;
3. School of Mathematics and Computer Sciences, & Institute of Mathematics and Interdisciplinary Sciences, Nanchang University, Nanchang 330031, China

收稿日期:2024-10-10 修回日期:2025-04-15 出版日期:2026-01-25 发布日期:2026-05-22
基金资助:
fund: This work was supported by the National Natural Science Foundation of China (12401279, 12371219), the Double-Thousand Plan of Jiangxi Province (jxsq2023201115) and the Academic and Technical Leaders Training Plan of Jiangxi Province (20212BCJ23027). Mengdi TONG, E-mail: 355500210004@email.ncu.edu.cn; Xue Wang, E-mail: xuewa@amss.ac.cn

GLOBAL STRONG SOLUTIONS TO THE PLANAR COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH DEGENERATE HEAT-CONDUCTIVITY IN THE HALF-LINE

Mengdi TONG¹, Xue Wang², Rong ZHANG^3,*

1. School of Mathematics and Computer Sciences, Nanchang University, Nanchang 330031, China;
2. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;
3. School of Mathematics and Computer Sciences, & Institute of Mathematics and Interdisciplinary Sciences, Nanchang University, Nanchang 330031, China

Received:2024-10-10 Revised:2025-04-15 Online:2026-01-25 Published:2026-05-22
Contact: * Rong ZHANG, E-mail: rzhang0921@gmail.com
Supported by:
National Natural Science Foundation of China (12401279, 12371219), the Double-Thousand Plan of Jiangxi Province (jxsq2023201115) and the Academic and Technical Leaders Training Plan of Jiangxi Province (20212BCJ23027).

摘要/Abstract

摘要： This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line. In particular, the transverse magnetic field is assumed to satisfy the Neumann boundary condition, which was first investigated by Kazhikhov in 1987. We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data. More precisely, our result can be regarded as a natural generalization of Kazhikov's result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.

关键词: Magnetohydrodynamics, temperature-dependent heat conductivity, global strong solutions, half-line

Abstract: This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line. In particular, the transverse magnetic field is assumed to satisfy the Neumann boundary condition, which was first investigated by Kazhikhov in 1987. We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data. More precisely, our result can be regarded as a natural generalization of Kazhikov's result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.

Key words: Magnetohydrodynamics, temperature-dependent heat conductivity, global strong solutions, half-line

中图分类号:

35Q35

Mengdi TONG¹, Xue Wang², Rong ZHANG^3,*. GLOBAL STRONG SOLUTIONS TO THE PLANAR COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH DEGENERATE HEAT-CONDUCTIVITY IN THE HALF-LINE[J]. 数学物理学报(英文版), 2026, 46(1): 189-208.

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GLOBAL STRONG SOLUTIONS TO THE PLANAR COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH DEGENERATE HEAT-CONDUCTIVITY IN THE HALF-LINE

GLOBAL STRONG SOLUTIONS TO THE PLANAR COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH DEGENERATE HEAT-CONDUCTIVITY IN THE HALF-LINE

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