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

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED Journal of Mathematical Fluid Mechanics Pub Date : 2024-08-29 DOI:10.1007/s00021-024-00892-1

Wen Feng, Weinan Wang, Jiahong Wu

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引用次数: 0

摘要

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

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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来源期刊

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.