圆柱空间上扎哈罗夫-库兹涅佐夫方程的考奇问题的全局好求解性

Pub Date : 2024-01-22 DOI:10.58997/ejde.2024.05

Satoshi Osawa, Hideo Takaoka

{"title":"圆柱空间上扎哈罗夫-库兹涅佐夫方程的考奇问题的全局好求解性","authors":"Satoshi Osawa, Hideo Takaoka","doi":"10.58997/ejde.2024.05","DOIUrl":null,"url":null,"abstract":"We study the global well-posedness of the Zakharov-Kuznetsov equation on cylindrical spaces. Our goal is to establish the existence of global-in-time solutions below the energy class. To prove the results, we adapt the I-method to extend the local solutions globally in time. The main tool in our argument is multilinear estimates in the content of Bourgain's spaces. Using modified energies induced \nFor more information see https://ejde.math.txstate.edu/Volumes/2024/05/abstr.html","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global well-posedness for Cauchy problems of Zakharov-Kuznetsov equations on cylindrical spaces\",\"authors\":\"Satoshi Osawa, Hideo Takaoka\",\"doi\":\"10.58997/ejde.2024.05\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the global well-posedness of the Zakharov-Kuznetsov equation on cylindrical spaces. Our goal is to establish the existence of global-in-time solutions below the energy class. To prove the results, we adapt the I-method to extend the local solutions globally in time. The main tool in our argument is multilinear estimates in the content of Bourgain's spaces. Using modified energies induced \\nFor more information see https://ejde.math.txstate.edu/Volumes/2024/05/abstr.html\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-01-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.58997/ejde.2024.05\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.58997/ejde.2024.05","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了圆柱空间上扎哈罗夫-库兹涅佐夫方程的全局好求解性。我们的目标是建立低于能量级的全局时间解。为了证明这些结果，我们调整了 I 方法，以在时间上扩展局部解。我们论证的主要工具是布尔干空间内容中的多线性估计。更多信息请参见 https://ejde.math.txstate.edu/Volumes/2024/05/abstr.html。

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

微信好友朋友圈 QQ好友复制链接

Global well-posedness for Cauchy problems of Zakharov-Kuznetsov equations on cylindrical spaces

We study the global well-posedness of the Zakharov-Kuznetsov equation on cylindrical spaces. Our goal is to establish the existence of global-in-time solutions below the energy class. To prove the results, we adapt the I-method to extend the local solutions globally in time. The main tool in our argument is multilinear estimates in the content of Bourgain's spaces. Using modified energies induced For more information see https://ejde.math.txstate.edu/Volumes/2024/05/abstr.html

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