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

Huan Long; Suhui Ye; Huan Long; Suhui Ye

doi:10.3934/math.20241725

AIMS Mathematics

2024, Volume 9, Issue 12: 36371-36384. doi: 10.3934/math.20241725

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Research article

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

Received: 15 October 2024 Revised: 03 December 2024 Accepted: 17 December 2024 Published: 31 December 2024
MSC : 35A05, 35Q35, 76D03

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.
- magnetohydrodynamic equations,
- global solutions,
- Diophantine condition
Citation: Huan Long, Suhui Ye. Global well-posedness for the 2D MHD equations with only vertical velocity damping term[J]. AIMS Mathematics, 2024, 9(12): 36371-36384. doi: 10.3934/math.20241725

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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.

References

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