Constructing boundary layer approximations in rotating magnetohydrodynamic fluids within cylindrical domains
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,...
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025128 |
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| author | Guanglei Zhang Kexue Chen Yifei Jia |
| author_facet | Guanglei Zhang Kexue Chen Yifei Jia |
| author_sort | Guanglei Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e829fef301a9444fa63f29930fd6e78b |
| institution | DOAJ |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-e829fef301a9444fa63f29930fd6e78b2025-08-20T03:17:09ZengAIMS PressAIMS Mathematics2473-69882025-02-011022724274910.3934/math.2025128Constructing boundary layer approximations in rotating magnetohydrodynamic fluids within cylindrical domainsGuanglei Zhang0Kexue Chen1Yifei Jia2Department of Mathematics, Jinan University, Guangzhou, ChinaDepartment of Mathematics, Jinan University, Guangzhou, ChinaCollege of Mathematics and System Science, Xinjiang University, Urumqi, ChinaThis 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.https://www.aimspress.com/article/doi/10.3934/math.2025128magnetohydrodynamicsrotating dynamical systemekman-hartmann boundary layercylinder domainasymptotic behavior |
| spellingShingle | Guanglei Zhang Kexue Chen Yifei Jia Constructing boundary layer approximations in rotating magnetohydrodynamic fluids within cylindrical domains AIMS Mathematics magnetohydrodynamics rotating dynamical system ekman-hartmann boundary layer cylinder domain asymptotic behavior |
| title | Constructing boundary layer approximations in rotating magnetohydrodynamic fluids within cylindrical domains |
| title_full | Constructing boundary layer approximations in rotating magnetohydrodynamic fluids within cylindrical domains |
| title_fullStr | Constructing boundary layer approximations in rotating magnetohydrodynamic fluids within cylindrical domains |
| title_full_unstemmed | Constructing boundary layer approximations in rotating magnetohydrodynamic fluids within cylindrical domains |
| title_short | Constructing boundary layer approximations in rotating magnetohydrodynamic fluids within cylindrical domains |
| title_sort | constructing boundary layer approximations in rotating magnetohydrodynamic fluids within cylindrical domains |
| topic | magnetohydrodynamics rotating dynamical system ekman-hartmann boundary layer cylinder domain asymptotic behavior |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025128 |
| work_keys_str_mv | AT guangleizhang constructingboundarylayerapproximationsinrotatingmagnetohydrodynamicfluidswithincylindricaldomains AT kexuechen constructingboundarylayerapproximationsinrotatingmagnetohydrodynamicfluidswithincylindricaldomains AT yifeijia constructingboundarylayerapproximationsinrotatingmagnetohydrodynamicfluidswithincylindricaldomains |