JAMC

Article http://dx.doi.org/10.26855/jamc.2025.12.005

Stability Analysis of Boundary Layer for the 3D Parallel Pipe Magnetohydrodynamic Flows

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Zhijun Ji

School of Financial Mathematics and Statistics, Guangdong University of Finance, Guangzhou 510521, Guangdong, China.

*Corresponding author:Zhijun Ji

This paper is supported by Guangzhou Natural Science Foundation (Grant No. 2024A04J4507), Natural Science Foundation of Guangdong Province (Grant No.2023A1515012044), and Bureau of Education in Guangdong Province (Grant No. 2025ZDZX4046).

Published: December 30,2025

Abstract

This paper presents a rigorous mathematical analysis validating the boundary layer expansion for parallel pipe flows governed by the 3D incompressible MHD equations. The physical setup considers no-slip velocity conditions and perfectly conducting magnetic boundary conditions. The core contribution is the establishment of the convergence rates for the expansion in Sobolev norms. Specifically, it is proven that the error terms are bounded as O(ϵ^3/4) in L^∞ (0,T;L² (Ω)) norm and as O(ϵ^1/4) in the L^∞ (0,T; H¹ (Ω)) norm. These results provide a rigorous foundation for the asymptotic behavior of the MHD system, confirming that viscous magnetic fluids can be characterized by the boundary layer correction near the edge and the behavior of the ideal magnetic fluid far from the edge. The analysis thereby offers a firm theoretical framework for understanding the process of the vanishing of viscosity and magnetic diffusion.

Keywords

Boundary layer theory; Parallel pipe flow; MHD equations; Sobolev space

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How to cite this paper

Stability Analysis of Boundary Layer for the 3D Parallel Pipe Magnetohydrodynamic Flows

How to cite this paper: Zhijun Ji. (2025) Stability Analysis of Boundary Layer for the 3D Parallel Pipe Magnetohydrodynamic Flows. Journal of Applied Mathematics and Computation, 9(4), 258-265.

DOI: http://dx.doi.org/10.26855/jamc.2025.12.005