Global well-posedness for 2D non-resistive compressible MHD system in periodic domain
Global well-posedness for 2D non-resistive compressible MHD system in periodic domain
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DOI：
10.1016/j.jfa.2022.109602
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发表时间：
2022-06
影响因子：
1.7
通讯作者：
Jiahong Wu;Yi Zhu
中科院分区：
文献类型：
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作者：
Jiahong Wu;Yi Zhu
研究了周期区域中无磁扩散的二维可压缩磁流体动力学方程组。我们提出了一个系统的方法来建立光滑的解决方案时，初始数据接近背景磁场的整体存在性。此外，稳定性和大时间衰减率也得到了。当没有磁扩散时，磁场和密度由强迫输运方程控制，这里考虑的问题是困难的。本文实现了几个关键的意见和想法，以最大限度地提高由于隐藏的结构和相互作用的耗散。特别地，充分利用了背景磁场产生的弱平滑和稳定性以及速度场发散部分的额外正则化。与以往的工作相比，本文似乎是第一个调查这样的系统上的有界域和第一个解决这个问题的纯能量估计，这有助于减少在其他方法的复杂性。此外，本文将适定性与精确的大时间行为相结合，这种策略可以扩展到更高的维度。
This paper focuses on the 2D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion in a periodic domain. We present a systematic approach to establishing the global existence of smooth solutions when the initial data is close to a background magnetic field. In addition, stability and large-time decay rates are also obtained. When there is no magnetic diffusion, the magnetic field and the density are governed by forced transport equations and the problem considered here is difficult. This paper implements several key observations and ideas to maximize the enhanced dissipation due to hidden structures and interactions. In particular, the weak smoothing and stabilization generated by the background magnetic field and the extra regularization in the divergence part of the velocity field are fully exploited. Compared with the previous works, this paper appears to be the first to investigate such system on bounded domains and the first to solve this problem by pure energy estimates, which help reduce the complexity in other approaches. In addition, this paper combines the well-posedness with the precise large-time behavior, a strategy that can be extended to higher dimensions.