{"title":"临界Fourier-Besov-Morrey空间中二维次临界耗散拟地转方程的全局适定性和渐近性","authors":"Achraf Azanzal, Chakir Allalou null, Adil Abbassi","doi":"10.4208/jpde.v36.n1.1","DOIUrl":null,"url":null,"abstract":". In this paper, we study the subcritical dissipative quasi-geostrophic equation. By using the Littlewood Paley theory, Fourier analysis and standard techniques we prove that there exists v a unique global-in-time solution for small initial data be-longing to the critical Fourier-Besov-Morrey spaces FN 3 − 2 α + λ − 2 p p , λ , q . Moreover, we show the asymptotic behavior of the global solution v . i.e., k v ( t ) k FN 3 − 2 α + λ − 2 p p , λ , q decays to zero as time goes to infinity.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces\",\"authors\":\"Achraf Azanzal, Chakir Allalou null, Adil Abbassi\",\"doi\":\"10.4208/jpde.v36.n1.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this paper, we study the subcritical dissipative quasi-geostrophic equation. By using the Littlewood Paley theory, Fourier analysis and standard techniques we prove that there exists v a unique global-in-time solution for small initial data be-longing to the critical Fourier-Besov-Morrey spaces FN 3 − 2 α + λ − 2 p p , λ , q . Moreover, we show the asymptotic behavior of the global solution v . i.e., k v ( t ) k FN 3 − 2 α + λ − 2 p p , λ , q decays to zero as time goes to infinity.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/jpde.v36.n1.1\",\"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/10.4208/jpde.v36.n1.1","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
. 本文研究了亚临界耗散准地转方程。利用Littlewood Paley理论、傅里叶分析和标准技术,证明了在临界傅里叶- besov - morrey空间FN 3−2 α + λ−2 p p, λ, q下存在唯一的全局实时解。此外,我们还证明了全局解v的渐近性质。即k v (t) k FN 3−2 α + λ−2 p p, λ, q随着时间趋于无穷衰减为零。
Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces
. In this paper, we study the subcritical dissipative quasi-geostrophic equation. By using the Littlewood Paley theory, Fourier analysis and standard techniques we prove that there exists v a unique global-in-time solution for small initial data be-longing to the critical Fourier-Besov-Morrey spaces FN 3 − 2 α + λ − 2 p p , λ , q . Moreover, we show the asymptotic behavior of the global solution v . i.e., k v ( t ) k FN 3 − 2 α + λ − 2 p p , λ , q decays to zero as time goes to infinity.