Sobolev空间中可压缩磁流体边界层方程的长时间适定性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/dcds.2023133

Shengxin Li, Feng Xie

{"title":"Sobolev空间中可压缩磁流体边界层方程的长时间适定性","authors":"Shengxin Li, Feng Xie","doi":"10.3934/dcds.2023133","DOIUrl":null,"url":null,"abstract":"In this paper we consider the long time well-posedness of solutions to two-dimensional compressible magnetohydrodynamic (MHD) boundary layer equations. When the initial data is a small perturbation of a steady solution with size of $ \\varepsilon $, then the lifespan of solutions in Sobolev spaces is proved to be greater than $ \\varepsilon^{-\\frac43} $. And such a result can be extended to the case that both initial data and far-field state are small perturbations around the steady states. Moreover, it holds true for both isentropic and non-isentropic magnetohydrodynamic boundary layer equations.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Long time well-posedness of compressible magnetohydrodynamic boundary layer equations in Sobolev spaces\",\"authors\":\"Shengxin Li, Feng Xie\",\"doi\":\"10.3934/dcds.2023133\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we consider the long time well-posedness of solutions to two-dimensional compressible magnetohydrodynamic (MHD) boundary layer equations. When the initial data is a small perturbation of a steady solution with size of $ \\\\varepsilon $, then the lifespan of solutions in Sobolev spaces is proved to be greater than $ \\\\varepsilon^{-\\\\frac43} $. And such a result can be extended to the case that both initial data and far-field state are small perturbations around the steady states. Moreover, it holds true for both isentropic and non-isentropic magnetohydrodynamic boundary layer equations.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/dcds.2023133\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/dcds.2023133","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

本文考虑二维可压缩磁流体边界层方程解的长时间适定性。当初始数据是大小为$ \varepsilon $的稳定解的小扰动时，则证明了Sobolev空间中解的寿命大于$ \varepsilon^{-\frac43} $。这一结果可以推广到初始数据和远场状态都是围绕稳态的小扰动的情况。此外，它对等熵和非等熵磁流体边界层方程都成立。

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

Long time well-posedness of compressible magnetohydrodynamic boundary layer equations in Sobolev spaces

In this paper we consider the long time well-posedness of solutions to two-dimensional compressible magnetohydrodynamic (MHD) boundary layer equations. When the initial data is a small perturbation of a steady solution with size of $ \varepsilon $, then the lifespan of solutions in Sobolev spaces is proved to be greater than $ \varepsilon^{-\frac43} $. And such a result can be extended to the case that both initial data and far-field state are small perturbations around the steady states. Moreover, it holds true for both isentropic and non-isentropic magnetohydrodynamic boundary layer equations.

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.