Besov空间中FORQ方程解映射数据的连续性

IF 1.8 4区数学 Q1 MATHEMATICS

Differential and Integral Equations Pub Date : 2020-10-09 DOI:10.57262/die034-0506-295

J. Holmes, F. Tiglay, R. Thompson

{"title":"Besov空间中FORQ方程解映射数据的连续性","authors":"J. Holmes, F. Tiglay, R. Thompson","doi":"10.57262/die034-0506-295","DOIUrl":null,"url":null,"abstract":"For Besov spaces $B^s_{p,r}(\\rr)$ with $s>\\max\\{ 2 + \\frac1p , \\frac52\\} $, $p \\in (1,\\infty]$ and $r \\in [1 , \\infty)$, it is proved that the data-to-solution map for the FORQ equation is not uniformly continuous from $B^s_{p,r}(\\rr)$ to $C([0,T]; B^s_{p,r}(\\rr))$. The proof of non-uniform dependence is based on approximate solutions and the Littlewood-Paley decomposition.","PeriodicalId":50581,"journal":{"name":"Differential and Integral Equations","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2020-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Continuity of the data-to-solution map for the FORQ equation in Besov spaces\",\"authors\":\"J. Holmes, F. Tiglay, R. Thompson\",\"doi\":\"10.57262/die034-0506-295\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For Besov spaces $B^s_{p,r}(\\\\rr)$ with $s>\\\\max\\\\{ 2 + \\\\frac1p , \\\\frac52\\\\} $, $p \\\\in (1,\\\\infty]$ and $r \\\\in [1 , \\\\infty)$, it is proved that the data-to-solution map for the FORQ equation is not uniformly continuous from $B^s_{p,r}(\\\\rr)$ to $C([0,T]; B^s_{p,r}(\\\\rr))$. The proof of non-uniform dependence is based on approximate solutions and the Littlewood-Paley decomposition.\",\"PeriodicalId\":50581,\"journal\":{\"name\":\"Differential and Integral Equations\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2020-10-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential and Integral Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.57262/die034-0506-295\",\"RegionNum\":4,\"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":"Differential and Integral Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.57262/die034-0506-295","RegionNum":4,"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

对于含有$s>\max\{ 2 + \frac1p , \frac52\} $、$p \in (1,\infty]$和$r \in [1 , \infty)$的Besov空间$B^s_{p,r}(\rr)$，证明了FORQ方程的数据-解映射从$B^s_{p,r}(\rr)$到$C([0,T]; B^s_{p,r}(\rr))$不是一致连续的。非一致相关性的证明是基于近似解和Littlewood-Paley分解。

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

Continuity of the data-to-solution map for the FORQ equation in Besov spaces

For Besov spaces $B^s_{p,r}(\rr)$ with $s>\max\{ 2 + \frac1p , \frac52\} $, $p \in (1,\infty]$ and $r \in [1 , \infty)$, it is proved that the data-to-solution map for the FORQ equation is not uniformly continuous from $B^s_{p,r}(\rr)$ to $C([0,T]; B^s_{p,r}(\rr))$. The proof of non-uniform dependence is based on approximate solutions and the Littlewood-Paley decomposition.

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

Differential and Integral Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential and Integral Equations will publish carefully selected research papers on mathematical aspects of differential and integral equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new, and of interest to a substantial number of mathematicians working in these areas.