Stability for a System of the 2D Incompressible MHD Equations with Fractional Dissipation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-08-29 DOI:10.1007/s00021-024-00892-1

Wen Feng, Weinan Wang, Jiahong Wu

引用次数: 0

Abstract

Several fundamental problems on the 2D magnetohydrodynamic (MHD) equations with only magnetic diffusion (no velocity dissipation) remain open, especialy in the case when the spatial domain is the whole space \({\mathbb {R}}^2\). This paper establishes that, near a background magnetic field, any fractional dissipation in one direction in the velocity equation would allow us to establish the global existence and stability for perturbations near the background. The magnetic diffusion here is not required to be given by the standard Laplacian operator but any general fractional Laplacian with positive power.

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具有分数耗散的二维不可压缩多流体力学方程系统的稳定性

关于仅有磁扩散（无速度耗散）的二维磁流体力学（MHD）方程的几个基本问题仍未解决，特别是在空间域为整个空间（{\mathbb {R}}^2\ ）的情况下。本文证明，在背景磁场附近，速度方程中一个方向上的任何分数耗散都能让我们建立起背景附近扰动的全局存在性和稳定性。这里的磁扩散不需要由标准拉普拉斯算子给出，而是由任何具有正幂次的一般分数拉普拉斯算子给出。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.