非陷波渐近双曲流形上波的逆Strichartz估计及其应用

IF 2.1 2区数学 Q1 MATHEMATICS

Communications in Partial Differential Equations Pub Date : 2021-08-26 DOI:10.1080/03605302.2022.2047724

Y. Sire, C. Sogge, Chengbo Wang, Junyong Zhang

{"title":"非陷波渐近双曲流形上波的逆Strichartz估计及其应用","authors":"Y. Sire, C. Sogge, Chengbo Wang, Junyong Zhang","doi":"10.1080/03605302.2022.2047724","DOIUrl":null,"url":null,"abstract":"Abstract We provide reversed Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds using cluster estimates for spectral projectors proved previously in such generality. As a consequence, we solve a problem left open in Sire et al [Trans. AMS 373(2020):7639-7668] about the endpoint case for global well-posedness of nonlinear wave equations. We also provide estimates in this context for the maximal wave operator.","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"47 1","pages":"1124 - 1132"},"PeriodicalIF":2.1000,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Reversed Strichartz estimates for wave on non-trapping asymptotically hyperbolic manifolds and applications\",\"authors\":\"Y. Sire, C. Sogge, Chengbo Wang, Junyong Zhang\",\"doi\":\"10.1080/03605302.2022.2047724\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We provide reversed Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds using cluster estimates for spectral projectors proved previously in such generality. As a consequence, we solve a problem left open in Sire et al [Trans. AMS 373(2020):7639-7668] about the endpoint case for global well-posedness of nonlinear wave equations. We also provide estimates in this context for the maximal wave operator.\",\"PeriodicalId\":50657,\"journal\":{\"name\":\"Communications in Partial Differential Equations\",\"volume\":\"47 1\",\"pages\":\"1124 - 1132\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2021-08-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Partial Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/03605302.2022.2047724\",\"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":"Communications in Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/03605302.2022.2047724","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: 4

摘要

摘要我们利用先前证明的谱投影的聚类估计，为非陷波渐近双曲流形上的位移波方程提供了逆Strichartz估计。因此，我们解决了Sire等人[Trans.AMS 373（2020）：7639-7668]中留下的关于非线性波动方程的全局适定性的端点情况的问题。在这种情况下，我们还提供了对最大波算子的估计。

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

Reversed Strichartz estimates for wave on non-trapping asymptotically hyperbolic manifolds and applications

Abstract We provide reversed Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds using cluster estimates for spectral projectors proved previously in such generality. As a consequence, we solve a problem left open in Sire et al [Trans. AMS 373(2020):7639-7668] about the endpoint case for global well-posedness of nonlinear wave equations. We also provide estimates in this context for the maximal wave operator.

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

Communications in Partial Differential Equations 数学-数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal aims to publish high quality papers concerning any theoretical aspect of partial differential equations, as well as its applications to other areas of mathematics. Suitability of any paper is at the discretion of the editors. We seek to present the most significant advances in this central field to a wide readership which includes researchers and graduate students in mathematics and the more mathematical aspects of physics and engineering.