Constructing boundary layer approximations in rotating magnetohydrodynamic fluids within cylindrical domains

Guanglei Zhang; Kexue Chen; Yifei Jia; Guanglei Zhang; Kexue Chen; Yifei Jia

doi:10.3934/math.2025128

AIMS Mathematics

2025, Volume 10, Issue 2: 2724-2749. doi: 10.3934/math.2025128

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Constructing boundary layer approximations in rotating magnetohydrodynamic fluids within cylindrical domains

1.
Department of Mathematics, Jinan University, Guangzhou, China
2.
College of Mathematics and System Science, Xinjiang University, Urumqi, China

Received: 28 November 2024 Revised: 13 January 2025 Accepted: 23 January 2025 Published: 14 February 2025
MSC : 76D10, 76U05

This paper aims to investigate the effects of the Ekman-Hartmann boundary layer on rotating magnetohydrodynamics (MHD) within cylindrical domains, focusing on constructing approximate solutions within the boundary layer. We employed the multiscale analysis method to derive the approximate solutions, emphasizing the solutions at the cylinder's corners and lateral boundaries. Furthermore, we rigorously examined the asymptotic behavior of the rotating MHD flow in the limit case, proving its convergence to a two-dimensional damped and rotating dynamical system. These findings revealed the significant impact of high-speed rotation and strong magnetic fields on the structure and flow characteristics of the boundary layer, providing new insights into the dynamics of rotating MHD flows.
- magnetohydrodynamics,
- rotating dynamical system,
- Ekman-Hartmann boundary layer,
- cylinder domain,
- asymptotic behavior
Citation: Guanglei Zhang, Kexue Chen, Yifei Jia. Constructing boundary layer approximations in rotating magnetohydrodynamic fluids within cylindrical domains[J]. AIMS Mathematics, 2025, 10(2): 2724-2749. doi: 10.3934/math.2025128

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Abstract

This paper aims to investigate the effects of the Ekman-Hartmann boundary layer on rotating magnetohydrodynamics (MHD) within cylindrical domains, focusing on constructing approximate solutions within the boundary layer. We employed the multiscale analysis method to derive the approximate solutions, emphasizing the solutions at the cylinder's corners and lateral boundaries. Furthermore, we rigorously examined the asymptotic behavior of the rotating MHD flow in the limit case, proving its convergence to a two-dimensional damped and rotating dynamical system. These findings revealed the significant impact of high-speed rotation and strong magnetic fields on the structure and flow characteristics of the boundary layer, providing new insights into the dynamics of rotating MHD flows.

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