{"title":"Liouville-Type Theorems for the Stationary Ideal Magnetohydrodynamics Equations in \\(\\textbf{R}^n\\)","authors":"Lv Cai, Ning-An Lai, Anthony Suen, Manwai Yuen","doi":"10.1007/s00021-024-00902-2","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we establish Liouville-type theorems for the stationary ideal compressible magnetohydrodynamics system in <span>\\(\\textbf{R}^n\\)</span> with <span>\\(n\\in \\{1, 2, 3\\}\\)</span>. We address various cases when the finite energy condition is in force and the stationary density function <span>\\(\\rho \\)</span> satisfies <span>\\(\\displaystyle \\lim _{|x|\\rightarrow \\infty }\\rho (x)=\\rho _\\infty \\ge 0\\)</span>. Our proof relies heavily on the good structure of the nonlinear magnetic force term and the usage of well-chosen smooth cut-off test functions.\n</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-024-00902-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we establish Liouville-type theorems for the stationary ideal compressible magnetohydrodynamics system in \(\textbf{R}^n\) with \(n\in \{1, 2, 3\}\). We address various cases when the finite energy condition is in force and the stationary density function \(\rho \) satisfies \(\displaystyle \lim _{|x|\rightarrow \infty }\rho (x)=\rho _\infty \ge 0\). Our proof relies heavily on the good structure of the nonlinear magnetic force term and the usage of well-chosen smooth cut-off test functions.
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.
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