水平方向上只有分数级磁扩散的二维无粘MHD方程的稳定性

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-12-27 DOI:10.1016/j.aml.2024.109446

Yueyuan Zhong

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引用次数: 0

摘要

本文研究了一种特殊的二维磁流体动力学（MHD）系统，该系统在Ω=T×R域上只有水平方向上的分数阶磁扩散，且T=[0,1]为周期方框。由于缺乏速度耗散，这一稳定性问题不容忽视。在没有磁场存在的情况下，流体速度由二维不可压缩欧拉方程控制，其解增长相当快。然而，当耦合到这样的MHD系统中的磁场时，我们的结果显示出稳定效果。此外，我们将推导出解在水平方向上的指数衰减。

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 of 2D inviscid MHD equations with only fractional magnetic diffusion in the horizontal direction

This paper focuses on a special 2D magnetohydrodynamic (MHD) system with no viscosity and only fractional magnetic diffusion in the horizontal direction on the domain Ω=T×R and T=[0,1] be a periodic box. Due to the lack of the velocity dissipation, this stability problem is not trivial. Without the presence of a magnetic field, the fluid velocity is governed by the 2D incompressible Euler equation, and its solution grow rather rapidly. However, when coupled to the magnetic field in such an MHD system, our result in this paper then shows the stabilization effect. Moreover, we will derive the exponentially decay of solutions on horizontal direction.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.