三维非齐次不可压缩 MHD 方程组具边界的无粘极限问题

数学物理学报 ›› 2026, Vol. 46 ›› Issue (5): 1667-1684.

• • 下一篇

三维非齐次不可压缩 MHD 方程组具边界的无粘极限问题

陈鹏飞^*(), 陈清菡()

湖南省国家应用数学中心, 教育部智能计算与信息处理重点实验室,湖南省科学与工程计算与仿真重点实验室, 湘潭大学数学与计算科学学院湖南湘潭 411100

收稿日期:2024-08-20 修回日期:2025-04-20 出版日期:2026-10-26 发布日期:2026-09-07
通讯作者: 陈鹏飞 E-mail:cpf@xtu.edu.cn;hnqhchen@163.com
作者简介:陈清菡, E-mail: hnqhchen@163.com
基金资助:
国家自然科学基金(12371211);国家自然科学基金(11771300)

The Zero Parameter Limit for 3D Nonhomogeneous Incompressible MHD Equations with Boundary

Pengfei Chen^*(), Qinghan Chen()

National Center for Applied Mathematics in Hunan, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Hunan Xiangtan 411100

Received:2024-08-20 Revised:2025-04-20 Online:2026-10-26 Published:2026-09-07
Contact: Pengfei Chen E-mail:cpf@xtu.edu.cn;hnqhchen@163.com
Supported by:
NSFC(12371211);NSFC(11771300)

摘要/Abstract

摘要：

该文主要研究三维非齐次不可压缩磁流体动力学方程组具有物理边界条件情形的粘性消失极限问题. 具边界的情况下, 速度场和磁场分别满足涡旋滑移条件和完全绝缘条件. 作者在一般光滑有界区域中建立了初边值问题的弱解的整体存在性. 此外, 额外的初始边界条件 $\nabla\rho_0\cdot n = 0$ 在平坦区域对于提高边界条件的正则性以及证明局部强解的一致正则性方面起着非常重要的作用. 当粘性系数和磁耗散系数趋于零时, 作者在 $W^{2,p}(\Omega)$ 意义下建立了带收敛率的高阶收敛估计.

关键词: 非齐次不可压缩 MHD 方程, 粘性消失极限, 边界条件

Abstract:

This paper concerns the zero parameter limit problem for the 3-dimensional nonhomogeneous incompressible magnetohydrodynamic equations with physical boundary conditions. In presence of the boundary, the velocity field and the magnetic field fulfill the vorticity-slip and the perfect insulating condition, respectively. We establish a global in time weak solution for the initial-boundary-value problem in general smooth bounded domain. Moreover, for a flat domain, the additional initial boundary condition $\nabla\rho_0\cdot n=0$ plays a very important role in the improving the regularity of the boundary condition and the proof of uniform regularity of the local strong solution. As the viscosity and magnetic dissipation tend to zero, we establish the higher-order convergence estimate with a rate in sense of $W^{2,p}(\Omega)$.

Key words: nonhomogeneous incompressible MHD equations, the zero parameter limit, boundary conditions

中图分类号:

O175.2

陈鹏飞, 陈清菡. 三维非齐次不可压缩 MHD 方程组具边界的无粘极限问题[J]. 数学物理学报, 2026, 46(5): 1667-1684.

Pengfei Chen, Qinghan Chen. The Zero Parameter Limit for 3D Nonhomogeneous Incompressible MHD Equations with Boundary[J]. Acta mathematica scientia,Series A, 2026, 46(5): 1667-1684.

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三维非齐次不可压缩 MHD 方程组具边界的无粘极限问题

The Zero Parameter Limit for 3D Nonhomogeneous Incompressible MHD Equations with Boundary

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