Conditions for uniform regularity of compressible MHD system in small Alfvén and Mach numbers with tangential magnetic fields to the physical boundary

Yingzhi Du; Tao Luo; Xin Xu

doi:10.1016/j.jde.2025.113801

Conditions for uniform regularity of compressible MHD system in small Alfvén and Mach numbers with tangential magnetic fields to the physical boundary

Yingzhi Du
, Tao Luo^*
, Xin Xu

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

7 Downloads (CityUHK Scholars)

Abstract

This paper investigates the uniform regularity of solutions to the compressible magnetohydrodynamics (MHD) system in the half-space R₊³ in small Alfvén and Mach Numbers. The study focuses on the case where the magnetic field is tangential to the physical boundary, satisfying the perfect conducting boundary condition, while the velocity field adheres to a Navier-slip boundary condition. Under the condition that bounds the normal derivatives of the velocity and magnetic field uniformly in ϵ (the small Alfvén and Mach Numbers), we establish uniform estimates for the solutions in high-order conormal Sobolev norms. The results distinguish the previous works primarily addressing cases where the magnetic field is transversal to the boundary. © 2025 The Author(s).

Original language	English
Article number	113801
Number of pages	60
Journal	Journal of Differential Equations
Volume	453
Issue number	Part 1
Online published	3 Oct 2025
DOIs	https://doi.org/10.1016/j.jde.2025.113801
Publication status	Published - 5 Feb 2026

Funding

Luo's research is supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. 11307420). Xu's research is supported by Natural Science Foundation of China (Grant No. 12371229), Taishan Scholars Program (tsqn202312104) and the Natural Science Foundation of Shandong Province (Grant No. ZR2023YQ003).

Research Keywords

Alfvén number
Compressible MHD
Mach number
Perfect conducting boundary conditions
Uniform regularity

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This full text is made available under CC-BY 4.0. https://creativecommons.org/licenses/by/4.0/

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RGC-funded

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10.1016/j.jde.2025.113801

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title = "Conditions for uniform regularity of compressible MHD system in small Alfv{\'e}n and Mach numbers with tangential magnetic fields to the physical boundary",

abstract = "This paper investigates the uniform regularity of solutions to the compressible magnetohydrodynamics (MHD) system in the half-space R+3 in small Alfv{\'e}n and Mach Numbers. The study focuses on the case where the magnetic field is tangential to the physical boundary, satisfying the perfect conducting boundary condition, while the velocity field adheres to a Navier-slip boundary condition. Under the condition that bounds the normal derivatives of the velocity and magnetic field uniformly in ϵ (the small Alfv{\'e}n and Mach Numbers), we establish uniform estimates for the solutions in high-order conormal Sobolev norms. The results distinguish the previous works primarily addressing cases where the magnetic field is transversal to the boundary. {\textcopyright} 2025 The Author(s).",

keywords = "Alfv{\'e}n number, Compressible MHD, Mach number, Perfect conducting boundary conditions, Uniform regularity",

author = "Yingzhi Du and Tao Luo and Xin Xu",

year = "2026",

month = feb,

day = "5",

doi = "10.1016/j.jde.2025.113801",

language = "English",

volume = "453",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "Part 1",

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Conditions for uniform regularity of compressible MHD system in small Alfvén and Mach numbers with tangential magnetic fields to the physical boundary. / Du, Yingzhi ; Luo, Tao; Xu, Xin.
In: Journal of Differential Equations, Vol. 453, No. Part 1, 113801, 05.02.2026.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

TY - JOUR

T1 - Conditions for uniform regularity of compressible MHD system in small Alfvén and Mach numbers with tangential magnetic fields to the physical boundary

AU - Du, Yingzhi

AU - Luo, Tao

AU - Xu, Xin

PY - 2026/2/5

Y1 - 2026/2/5

N2 - This paper investigates the uniform regularity of solutions to the compressible magnetohydrodynamics (MHD) system in the half-space R+3 in small Alfvén and Mach Numbers. The study focuses on the case where the magnetic field is tangential to the physical boundary, satisfying the perfect conducting boundary condition, while the velocity field adheres to a Navier-slip boundary condition. Under the condition that bounds the normal derivatives of the velocity and magnetic field uniformly in ϵ (the small Alfvén and Mach Numbers), we establish uniform estimates for the solutions in high-order conormal Sobolev norms. The results distinguish the previous works primarily addressing cases where the magnetic field is transversal to the boundary. © 2025 The Author(s).

AB - This paper investigates the uniform regularity of solutions to the compressible magnetohydrodynamics (MHD) system in the half-space R+3 in small Alfvén and Mach Numbers. The study focuses on the case where the magnetic field is tangential to the physical boundary, satisfying the perfect conducting boundary condition, while the velocity field adheres to a Navier-slip boundary condition. Under the condition that bounds the normal derivatives of the velocity and magnetic field uniformly in ϵ (the small Alfvén and Mach Numbers), we establish uniform estimates for the solutions in high-order conormal Sobolev norms. The results distinguish the previous works primarily addressing cases where the magnetic field is transversal to the boundary. © 2025 The Author(s).

KW - Alfvén number

KW - Compressible MHD

KW - Mach number

KW - Perfect conducting boundary conditions

KW - Uniform regularity

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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-105017890995&origin=recordpage

U2 - 10.1016/j.jde.2025.113801

DO - 10.1016/j.jde.2025.113801

M3 - RGC 21 - Publication in refereed journal

SN - 0022-0396

VL - 453

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - Part 1

M1 - 113801

ER -

Conditions for uniform regularity of compressible MHD system in small Alfvén and Mach numbers with tangential magnetic fields to the physical boundary

Abstract

Funding

Research Keywords

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GRF: Long Time Well-Posedness and Dynamics for the Plasma-Vacuum Interface Problem in Magnetohydrodynamics (MHD) Nonlinear Partial Differential Equations.

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Conditions for uniform regularity of compressible MHD system in small Alfvén and Mach numbers with tangential magnetic fields to the physical boundary

Abstract

Funding

Research Keywords

Publisher's Copyright Statement

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

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GRF: Long Time Well-Posedness and Dynamics for the Plasma-Vacuum Interface Problem in Magnetohydrodynamics (MHD) Nonlinear Partial Differential Equations.

Cite this