{"title":"端点临界triiebel - lizorkin空间中不可压缩欧拉方程解的时间正则性 $$F^{d+1}_{1, \\infty }(\\mathbb {R}^d)$$","authors":"Hee Chul Pak","doi":"10.1007/s00028-023-00927-6","DOIUrl":null,"url":null,"abstract":"<p>An evidence of temporal discontinuity of the solution in <span>\\(F^s_{1, \\infty }(\\mathbb {R}^d)\\)</span> is presented, which implies the ill-posedness of the Cauchy problem for the Euler equations. Continuity and weak-type continuity of the solutions in related spaces are also discussed.\n</p>","PeriodicalId":51083,"journal":{"name":"Journal of Evolution Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Temporal regularity of the solution to the incompressible Euler equations in the end-point critical Triebel–Lizorkin space $$F^{d+1}_{1, \\\\infty }(\\\\mathbb {R}^d)$$\",\"authors\":\"Hee Chul Pak\",\"doi\":\"10.1007/s00028-023-00927-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>An evidence of temporal discontinuity of the solution in <span>\\\\(F^s_{1, \\\\infty }(\\\\mathbb {R}^d)\\\\)</span> is presented, which implies the ill-posedness of the Cauchy problem for the Euler equations. Continuity and weak-type continuity of the solutions in related spaces are also discussed.\\n</p>\",\"PeriodicalId\":51083,\"journal\":{\"name\":\"Journal of Evolution Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-11-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Evolution Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00028-023-00927-6\",\"RegionNum\":3,\"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":"Journal of Evolution Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00028-023-00927-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Temporal regularity of the solution to the incompressible Euler equations in the end-point critical Triebel–Lizorkin space $$F^{d+1}_{1, \infty }(\mathbb {R}^d)$$
An evidence of temporal discontinuity of the solution in \(F^s_{1, \infty }(\mathbb {R}^d)\) is presented, which implies the ill-posedness of the Cauchy problem for the Euler equations. Continuity and weak-type continuity of the solutions in related spaces are also discussed.
期刊介绍：
The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications.
Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field.
Particular topics covered by the journal are:
Linear and Nonlinear Semigroups
Parabolic and Hyperbolic Partial Differential Equations
Reaction Diffusion Equations
Deterministic and Stochastic Control Systems
Transport and Population Equations
Volterra Equations
Delay Equations
Stochastic Processes and Dirichlet Forms
Maximal Regularity and Functional Calculi
Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations
Evolution Equations in Mathematical Physics
Elliptic Operators
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