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Research Article | Open Access

Global well-posedness for the 2D MHD equations with only vertical velocity damping term

Huan Long( ), Suhui Ye
School of Mathematical Sciences, Geomathematics Key Laboratory of Sichuan Province, Chengdu University of Technology, Chengdu 610059, China
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Abstract

This paper concerns two-dimensional (2D) incompressible magnetohydrodynamic (MHD) equations without magnetic diffusion with only vertical velocity damping term in the periodic domain. We prove the stability and decay rate for smooth solutions on perturbations near a background magnetic field of the system under the assumptions that the initial magnetic field satisfies the Diophantine condition.

Keywords

magnetohydrodynamic equationsglobal solutionsDiophantine condition
CLC number: 35A05, 35Q35, 76D03

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AIMS Mathematics
Volume 9 Issue 12,
December 2024
Pages 36371-36384
DOI: 10.3934/math.20241725

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Cite this article:
Long H, Ye S. Global well-posedness for the 2D MHD equations with only vertical velocity damping term. AIMS Mathematics, 2024, 9(12): 36371-36384. https://doi.org/10.3934/math.20241725

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Received: 15 October 2024
Revised: 03 December 2024
Accepted: 17 December 2024
Published: 15 December 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)