二维欧拉方程涡斑解的存在性和规律性

IF 1.2 2区数学 Q1 MATHEMATICS

Indiana University Mathematics Journal Pub Date : 2022-11-15 DOI:10.1512/iumj.2022.71.9091

Razvan-Octavian Radu

{"title":"二维欧拉方程涡斑解的存在性和规律性","authors":"Razvan-Octavian Radu","doi":"10.1512/iumj.2022.71.9091","DOIUrl":null,"url":null,"abstract":". In [3], Bertozzi and Constantin formulate the vortex patch problem in the level-set framework and prove a priori estimates for this active scalar equation. By extending the tools used to prove these estimates, we construct solutions and show propagation of higher H¨older regularity. This constitutes a proof of the regularity of vortex patches, carried out solely in the level-set framework.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Existence and regularity for vortex patch solutions of the 2D Euler equations\",\"authors\":\"Razvan-Octavian Radu\",\"doi\":\"10.1512/iumj.2022.71.9091\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In [3], Bertozzi and Constantin formulate the vortex patch problem in the level-set framework and prove a priori estimates for this active scalar equation. By extending the tools used to prove these estimates, we construct solutions and show propagation of higher H¨older regularity. This constitutes a proof of the regularity of vortex patches, carried out solely in the level-set framework.\",\"PeriodicalId\":50369,\"journal\":{\"name\":\"Indiana University Mathematics Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2022-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indiana University Mathematics Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1512/iumj.2022.71.9091\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indiana University Mathematics Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1512/iumj.2022.71.9091","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 3

摘要

．在[3]中，Bertozzi和Constantin在水平集框架中构造了涡旋斑块问题，并证明了该活动标量方程的先验估计。通过扩展用于证明这些估计的工具，我们构造了解并展示了更高H - old正则性的传播。这构成了旋涡斑块的规律性的证明，仅在水平集框架中进行。

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

Existence and regularity for vortex patch solutions of the 2D Euler equations

. In [3], Bertozzi and Constantin formulate the vortex patch problem in the level-set framework and prove a priori estimates for this active scalar equation. By extending the tools used to prove these estimates, we construct solutions and show propagation of higher H¨older regularity. This constitutes a proof of the regularity of vortex patches, carried out solely in the level-set framework.

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