{"title":"欧拉方程的空间拟周期解","authors":"Xu Sun, Peter Topalov","doi":"10.1007/s00021-023-00804-9","DOIUrl":null,"url":null,"abstract":"<div><p>We develop a framework for studying quasi-periodic maps and diffeomorphisms on <span>\\({\\mathbb {R}}^n\\)</span>. As an application, we prove that the Euler equation is locally well posed in a space of quasi-periodic vector fields on <span>\\({\\mathbb {R}}^n\\)</span>. In particular, the equation preserves the spatial quasi-periodicity of the initial data. Several results on the analytic dependence of solutions on the time and the initial data are proved.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"25 3","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-023-00804-9.pdf","citationCount":"0","resultStr":"{\"title\":\"Spatially Quasi-Periodic Solutions of the Euler Equation\",\"authors\":\"Xu Sun, Peter Topalov\",\"doi\":\"10.1007/s00021-023-00804-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We develop a framework for studying quasi-periodic maps and diffeomorphisms on <span>\\\\({\\\\mathbb {R}}^n\\\\)</span>. As an application, we prove that the Euler equation is locally well posed in a space of quasi-periodic vector fields on <span>\\\\({\\\\mathbb {R}}^n\\\\)</span>. In particular, the equation preserves the spatial quasi-periodicity of the initial data. Several results on the analytic dependence of solutions on the time and the initial data are proved.</p></div>\",\"PeriodicalId\":649,\"journal\":{\"name\":\"Journal of Mathematical Fluid Mechanics\",\"volume\":\"25 3\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00021-023-00804-9.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/s00021-023-00804-9\",\"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/s00021-023-00804-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Spatially Quasi-Periodic Solutions of the Euler Equation
We develop a framework for studying quasi-periodic maps and diffeomorphisms on \({\mathbb {R}}^n\). As an application, we prove that the Euler equation is locally well posed in a space of quasi-periodic vector fields on \({\mathbb {R}}^n\). In particular, the equation preserves the spatial quasi-periodicity of the initial data. Several results on the analytic dependence of solutions on the time and the initial data are proved.
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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