@article{Long2024, 
author = {Huan Long and Suhui Ye},
title = {Global well-posedness for the 2D MHD equations with only vertical velocity damping term},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {36371-36384},
keywords = {magnetohydrodynamic equations, global solutions, Diophantine condition},
url = {https://www.sciopen.com/article/10.3934/math.20241725},
doi = {10.3934/math.20241725},
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.}
}