{"title":"可压缩纳维-斯托克斯方程球面对称解的渐近行为走向静止波","authors":"Itsuko Hashimoto, Shinya Nishibata, Souhei Sugizaki","doi":"10.1007/s00021-024-00885-0","DOIUrl":null,"url":null,"abstract":"<div><p>The present paper studies an asymptotic behavior of a spherically symmetric solution on the exterior domain of an unit ball for the compressible Navier–Stokes equation, describing a motion of viscous barotropic gas. Especially we study outflow problem, that is, the fluid blows out through boundary. Precisely we show an asymptotic stability of a spherically symmetric stationary solutions provided that an initial disturbance of the stationary solution is sufficiently small in the Sobolev space.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 4","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotic Behavior of Spherically Symmetric Solutions to the Compressible Navier–Stokes Equation Towards Stationary Waves\",\"authors\":\"Itsuko Hashimoto, Shinya Nishibata, Souhei Sugizaki\",\"doi\":\"10.1007/s00021-024-00885-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The present paper studies an asymptotic behavior of a spherically symmetric solution on the exterior domain of an unit ball for the compressible Navier–Stokes equation, describing a motion of viscous barotropic gas. Especially we study outflow problem, that is, the fluid blows out through boundary. Precisely we show an asymptotic stability of a spherically symmetric stationary solutions provided that an initial disturbance of the stationary solution is sufficiently small in the Sobolev space.</p></div>\",\"PeriodicalId\":649,\"journal\":{\"name\":\"Journal of Mathematical Fluid Mechanics\",\"volume\":\"26 4\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-08-05\",\"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/s00021-024-00885-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-024-00885-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Asymptotic Behavior of Spherically Symmetric Solutions to the Compressible Navier–Stokes Equation Towards Stationary Waves
The present paper studies an asymptotic behavior of a spherically symmetric solution on the exterior domain of an unit ball for the compressible Navier–Stokes equation, describing a motion of viscous barotropic gas. Especially we study outflow problem, that is, the fluid blows out through boundary. Precisely we show an asymptotic stability of a spherically symmetric stationary solutions provided that an initial disturbance of the stationary solution is sufficiently small in the Sobolev space.
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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