环空中欧拉-泊松系统跨音速激波解的动力稳定性

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2025-09-05 DOI:10.1007/s00021-025-00961-z

Qifeng Bai, Yuanyuan Xing

{"title":"环空中欧拉-泊松系统跨音速激波解的动力稳定性","authors":"Qifeng Bai, Yuanyuan Xing","doi":"10.1007/s00021-025-00961-z","DOIUrl":null,"url":null,"abstract":"<div><p>This paper concerns the Euler-Poisson system in an annulus with finite radius. The dynamical stability of radially symmetric transonic shock solutions to the Euler-Poisson system is transformed into the global well-posedness of a free boundary problem for a second-order quasilinear hyperbolic equation. One of the crucial ingredients of the analysis is to establish an energy estimate for the associated initial boundary value problem. The steady radial transonic shock solutions are proved to be dynamically and exponentially stable with respect to small perturbations of the initial data.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"27 4","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dynamical Stability of Transonic Shock Solutions to Euler-Poisson System in an Annulus\",\"authors\":\"Qifeng Bai, Yuanyuan Xing\",\"doi\":\"10.1007/s00021-025-00961-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper concerns the Euler-Poisson system in an annulus with finite radius. The dynamical stability of radially symmetric transonic shock solutions to the Euler-Poisson system is transformed into the global well-posedness of a free boundary problem for a second-order quasilinear hyperbolic equation. One of the crucial ingredients of the analysis is to establish an energy estimate for the associated initial boundary value problem. The steady radial transonic shock solutions are proved to be dynamically and exponentially stable with respect to small perturbations of the initial data.</p></div>\",\"PeriodicalId\":649,\"journal\":{\"name\":\"Journal of Mathematical Fluid Mechanics\",\"volume\":\"27 4\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2025-09-05\",\"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/s00021-025-00961-z\",\"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/s00021-025-00961-z","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

摘要

本文研究了有限半径环空中的欧拉-泊松系统。将欧拉-泊松系统径向对称跨音速激波解的动力学稳定性转化为二阶拟线性双曲型方程自由边界问题的全局适定性。该分析的关键组成部分之一是为相关的初始边值问题建立能量估计。证明了稳态径向跨音速激波解在初始数据的小扰动下是动态和指数稳定的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Dynamical Stability of Transonic Shock Solutions to Euler-Poisson System in an Annulus

This paper concerns the Euler-Poisson system in an annulus with finite radius. The dynamical stability of radially symmetric transonic shock solutions to the Euler-Poisson system is transformed into the global well-posedness of a free boundary problem for a second-order quasilinear hyperbolic equation. One of the crucial ingredients of the analysis is to establish an energy estimate for the associated initial boundary value problem. The steady radial transonic shock solutions are proved to be dynamically and exponentially stable with respect to small perturbations of the initial data.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

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.