GLOBAL WELL-POSEDNESS FOR THE 3D INCOMPRESSIBLE HEAT-CONDUCTING MAGNETOHYDRODYNAMIC FLOWS WITH TEMPERATURE-DEPENDENT COEFFICIENTS

doi:10.1007/s10473-025-0312-6

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (3): 951-981.doi: 10.1007/s10473-025-0312-6

GLOBAL WELL-POSEDNESS FOR THE 3D INCOMPRESSIBLE HEAT-CONDUCTING MAGNETOHYDRODYNAMIC FLOWS WITH TEMPERATURE-DEPENDENT COEFFICIENTS

Qingyan LI¹, Zhenhua GUO^2,†

1. School of Sciences, Chang'an University, Xi'an 710064, China;
2. Center for Applied Mathematics of Guangxi, School of Mathematics and Information Science, Guangxi University, Nanning 530004, China

收稿日期:2023-10-05 修回日期:2024-08-06 出版日期:2025-05-25 发布日期:2025-09-30

GLOBAL WELL-POSEDNESS FOR THE 3D INCOMPRESSIBLE HEAT-CONDUCTING MAGNETOHYDRODYNAMIC FLOWS WITH TEMPERATURE-DEPENDENT COEFFICIENTS

Qingyan LI¹, Zhenhua GUO^2,†

1. School of Sciences, Chang'an University, Xi'an 710064, China;
2. Center for Applied Mathematics of Guangxi, School of Mathematics and Information Science, Guangxi University, Nanning 530004, China

Received:2023-10-05 Revised:2024-08-06 Online:2025-05-25 Published:2025-09-30
Contact: ^†Zhenhua GUO, E-mail: zhguo@gxu.edu.cn
About author:Qingyan LI, E-mail: qyli22@126.com
Supported by:
National Natural Science Foundation of China (No.11931013), the Natural Science Foundation of Guangxi Province (No.2022GXNSFDA035078) and the Foundamental Research Funds for the Central Universities, CHD (No.300102122115).

摘要/Abstract

摘要： In this paper, we consider an initial boundary value problem for the nonhomogeneous heat-conducting magnetohydrodynamic fluids when the viscosity $\mu$, magnetic diffusivity $\nu$ and heat conductivity $\kappa$ depend on the temperature $\theta$ according to $\mu(\theta)=\theta^{\alpha}$, $\ \kappa(\theta)=\theta^{\beta}$, $\nu(\theta)=\theta^{\gamma}$, with $\alpha$, $\gamma>0$, $\beta\geq 0$. We prove the global existence of a unique strong solution provided that $\|\sqrt{\rho_0}u_0\|_{L^2}^2+\|H_0\|_{L^2}^2+\beta\|\sqrt{\rho_0}\theta_0\|_{L^2}^2$ is suitably small. In addition, we also get some results of the large-time behavior and exponential decay estimates.

关键词: incompressible heat-conducting magnetohydrodynamic equations, temperature-dependent coefficients, strong solutions, global existence, exponential decay

Abstract: In this paper, we consider an initial boundary value problem for the nonhomogeneous heat-conducting magnetohydrodynamic fluids when the viscosity $\mu$, magnetic diffusivity $\nu$ and heat conductivity $\kappa$ depend on the temperature $\theta$ according to $\mu(\theta)=\theta^{\alpha}$, $\ \kappa(\theta)=\theta^{\beta}$, $\nu(\theta)=\theta^{\gamma}$, with $\alpha$, $\gamma>0$, $\beta\geq 0$. We prove the global existence of a unique strong solution provided that $\|\sqrt{\rho_0}u_0\|_{L^2}^2+\|H_0\|_{L^2}^2+\beta\|\sqrt{\rho_0}\theta_0\|_{L^2}^2$ is suitably small. In addition, we also get some results of the large-time behavior and exponential decay estimates.

Key words: incompressible heat-conducting magnetohydrodynamic equations, temperature-dependent coefficients, strong solutions, global existence, exponential decay

中图分类号:

35Q35

Qingyan LI, Zhenhua GUO. GLOBAL WELL-POSEDNESS FOR THE 3D INCOMPRESSIBLE HEAT-CONDUCTING MAGNETOHYDRODYNAMIC FLOWS WITH TEMPERATURE-DEPENDENT COEFFICIENTS[J]. 数学物理学报(英文版), 2025, 45(3): 951-981.

Qingyan LI, Zhenhua GUO. GLOBAL WELL-POSEDNESS FOR THE 3D INCOMPRESSIBLE HEAT-CONDUCTING MAGNETOHYDRODYNAMIC FLOWS WITH TEMPERATURE-DEPENDENT COEFFICIENTS[J]. Acta mathematica scientia,Series B, 2025, 45(3): 951-981.

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GLOBAL WELL-POSEDNESS FOR THE 3D INCOMPRESSIBLE HEAT-CONDUCTING MAGNETOHYDRODYNAMIC FLOWS WITH TEMPERATURE-DEPENDENT COEFFICIENTS

GLOBAL WELL-POSEDNESS FOR THE 3D INCOMPRESSIBLE HEAT-CONDUCTING MAGNETOHYDRODYNAMIC FLOWS WITH TEMPERATURE-DEPENDENT COEFFICIENTS

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