{"title":"The Optimal Temporal Decay Rates for Compressible Hall-magnetohydrodynamics System","authors":"Shengbin Fu, Weiwei Wang","doi":"10.1007/s00021-023-00820-9","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we are interested in the global well-posedness of the strong solutions to the Cauchy problem on the compressible magnetohydrodynamics system with Hall effect. Moreover, we establish the convergence rates of the above solutions trending towards the constant equilibrium <span>\\(({\\bar{\\rho }},0,\\bar{\\textbf{B}})\\)</span>, provided that the initial perturbation belonging to <span>\\(H^3({\\mathbb {R}}^3) \\cap B_{2, \\infty }^{-s}({\\mathbb {R}}^3)\\)</span> for <span>\\(s \\in (0,\\frac{3}{2}]\\)</span> is sufficiently small.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 4","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2023-08-26","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/s00021-023-00820-9","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 are interested in the global well-posedness of the strong solutions to the Cauchy problem on the compressible magnetohydrodynamics system with Hall effect. Moreover, we establish the convergence rates of the above solutions trending towards the constant equilibrium \(({\bar{\rho }},0,\bar{\textbf{B}})\), provided that the initial perturbation belonging to \(H^3({\mathbb {R}}^3) \cap B_{2, \infty }^{-s}({\mathbb {R}}^3)\) for \(s \in (0,\frac{3}{2}]\) is sufficiently small.
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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