论文标题
周期域中2D不可压缩的MHD系统的全球适应性
Global well-posedness for 2D non-resistive compressible MHD system in periodic domain
论文作者
论文摘要
本文重点介绍了2D可压缩的磁流体动力学（MHD）方程，而无需在周期域中进行磁扩散。当初始数据接近背景磁场时，我们提出了一种系统的方法来确定平滑解决方案的全局存在。另外，还获得了稳定性和大衰减率。当没有磁扩散时，磁场和密度受强制传输方程的控制，此处考虑的问题很困难。本文实施了几种关键观察和思想，以最大程度地提高由于隐藏的结构和互动而引起的增强耗散。特别是，由背景磁场产生的弱平滑和稳定化以及速度场差异部分中的额外正则化被充分利用。与以前的作品相比，本文似乎是第一个在有限域中研究此系统的文章，也是第一个通过纯能量估计来解决此问题的系统，这有助于降低其他方法的复杂性。此外，本文结合了良好的大型行为，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.
