{"title":"贝索夫空间中的纳维-斯托克斯方程和欧拉方程的假定性","authors":"Yanghai Yu, Fang Liu","doi":"10.21136/AM.2024.0089-24","DOIUrl":null,"url":null,"abstract":"<div><p>We construct a new initial data to prove the ill-posedness of both Navier-Stokes and Euler equations in weaker Besov spaces in the sense that the solution maps to these equations starting from <i>u</i><sub>0</sub> are discontinuous at <i>t</i> = 0.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 6","pages":"757 - 767"},"PeriodicalIF":0.6000,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Ill-posedness for the Navier-Stokes and Euler equations in Besov spaces\",\"authors\":\"Yanghai Yu, Fang Liu\",\"doi\":\"10.21136/AM.2024.0089-24\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We construct a new initial data to prove the ill-posedness of both Navier-Stokes and Euler equations in weaker Besov spaces in the sense that the solution maps to these equations starting from <i>u</i><sub>0</sub> are discontinuous at <i>t</i> = 0.</p></div>\",\"PeriodicalId\":55505,\"journal\":{\"name\":\"Applications of Mathematics\",\"volume\":\"69 6\",\"pages\":\"757 - 767\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applications of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.21136/AM.2024.0089-24\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applications of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.21136/AM.2024.0089-24","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Ill-posedness for the Navier-Stokes and Euler equations in Besov spaces
We construct a new initial data to prove the ill-posedness of both Navier-Stokes and Euler equations in weaker Besov spaces in the sense that the solution maps to these equations starting from u0 are discontinuous at t = 0.
期刊介绍：
Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering.
The main topics covered include:
- Mechanics of Solids;
- Fluid Mechanics;
- Electrical Engineering;
- Solutions of Differential and Integral Equations;
- Mathematical Physics;
- Optimization;
- Probability
Mathematical Statistics.
The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.
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