Stability and Sharp Decay Estimates for 3D MHD Equations with Only Vertical Dissipation Near a Background Magnetic Field
Abstract
This paper is concerned with the stability and large-time behavior of 3D incompressible MHD equations with only vertical dissipation near a background magnetic field. By making full use of the dissipation generated by the background magnetic field, we first establish the global stability of the solutions in -norm. Then, the optimal decay rates of the solutions are obtained, which are consistent with the 2D classical heat equation. Moreover, some enhanced decay rates of are also achieved. In other words, the decay estimates of the second or third component of velocity/magnetic field coincide with those of 2D heat kernel, while the first component behaves like the 3D heat kernel. This is mainly due to the divergence-free condition and the anisotropic structure. The results obtained improve the previous ones due to Lin-Wu-Zhu [24,25].
Keywords
Cite
@article{arxiv.2403.07293,
title = {Stability and Sharp Decay Estimates for 3D MHD Equations with Only Vertical Dissipation Near a Background Magnetic Field},
author = {Suhua Lai and Jiahong Wu and Jianwen Zhang and Xiaokui Zhao},
journal= {arXiv preprint arXiv:2403.07293},
year = {2024}
}