{"title":"Stability of 2D inviscid MHD equations with only fractional magnetic diffusion in the horizontal direction","authors":"Yueyuan Zhong","doi":"10.1016/j.aml.2024.109446","DOIUrl":null,"url":null,"abstract":"<div><div>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 <span><math><mrow><mi>Ω</mi><mo>=</mo><mi>T</mi><mo>×</mo><mi>R</mi></mrow></math></span> and <span><math><mrow><mi>T</mi><mo>=</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span> 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.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109446"},"PeriodicalIF":2.8000,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S089396592400466X","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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 and 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.
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.
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