{"title":"三维普朗特边界层方程的 Gevrey-2 长期存在解","authors":"Xinghong Pan, Chao-Jiang Xu","doi":"10.4310/cms.2024.v22.n5.a3","DOIUrl":null,"url":null,"abstract":"For the three dimensional Prandtl boundary layer equations, we will show that for arbitrary $M$ and sufficiently small $\\epsilon$, the lifespan of the Gevrey-2 solution is at least of size $\\epsilon^{-M}$ if the initial data lies in suitable Gevrey-2 spaces with size of $\\epsilon$.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Long-time existence of Gevrey-2 solutions to the 3D Prandtl boundary layer equations\",\"authors\":\"Xinghong Pan, Chao-Jiang Xu\",\"doi\":\"10.4310/cms.2024.v22.n5.a3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For the three dimensional Prandtl boundary layer equations, we will show that for arbitrary $M$ and sufficiently small $\\\\epsilon$, the lifespan of the Gevrey-2 solution is at least of size $\\\\epsilon^{-M}$ if the initial data lies in suitable Gevrey-2 spaces with size of $\\\\epsilon$.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/cms.2024.v22.n5.a3\",\"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":"100","ListUrlMain":"https://doi.org/10.4310/cms.2024.v22.n5.a3","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Long-time existence of Gevrey-2 solutions to the 3D Prandtl boundary layer equations
For the three dimensional Prandtl boundary layer equations, we will show that for arbitrary $M$ and sufficiently small $\epsilon$, the lifespan of the Gevrey-2 solution is at least of size $\epsilon^{-M}$ if the initial data lies in suitable Gevrey-2 spaces with size of $\epsilon$.
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.
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