{"title":"On the Steady Flows of Viscous Compressible Magnetohydrodynamic Equations in an Infinite Horizontal Layer","authors":"Rachid Benabidallah, François Ebobisse","doi":"10.1007/s00021-024-00881-4","DOIUrl":null,"url":null,"abstract":"<div><p>We consider in an infinite horizontal layer the stationary motion of a viscous compressible fluid in a magnetic field subject to the gravitational force, where the Dirichlet boundary condition for the velocity and similar but non-homogeneous and large enough conditions for the magnetic field are assumed. Existence of a stationary solution in a neighborhood close to the equilibrium state is obtained in Sobolev spaces as limit of a sequence of fixed points of some suitable operators.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 3","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00881-4.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-024-00881-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
We consider in an infinite horizontal layer the stationary motion of a viscous compressible fluid in a magnetic field subject to the gravitational force, where the Dirichlet boundary condition for the velocity and similar but non-homogeneous and large enough conditions for the magnetic field are assumed. Existence of a stationary solution in a neighborhood close to the equilibrium state is obtained in Sobolev spaces as limit of a sequence of fixed points of some suitable operators.
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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