{"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}
引用次数: 3
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.
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.