{"title":"修正卡马萨-霍姆方程在\\(B_{\\infty ,1}^0\\) 中的考奇问题的非确定性","authors":"Zhen He, Zhaoyang Yin","doi":"10.1007/s00021-024-00903-1","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we prove the norm inflation and get the ill-posedness for the modified Camassa-Holm equation in <span>\\(B_{\\infty ,1}^0\\)</span>. Therefore we completed all well-posedness and ill-posedness problem for the modified Camassa-Holm equation in all critical spaces <span>\\(B_{p,1}^\\frac{1}{p}\\)</span> with <span>\\(p\\in [1,\\infty ]\\)</span>.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 4","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Ill-Posedness for the Cauchy Problem of the Modified Camassa-Holm Equation in \\\\(B_{\\\\infty ,1}^0\\\\)\",\"authors\":\"Zhen He, Zhaoyang Yin\",\"doi\":\"10.1007/s00021-024-00903-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we prove the norm inflation and get the ill-posedness for the modified Camassa-Holm equation in <span>\\\\(B_{\\\\infty ,1}^0\\\\)</span>. Therefore we completed all well-posedness and ill-posedness problem for the modified Camassa-Holm equation in all critical spaces <span>\\\\(B_{p,1}^\\\\frac{1}{p}\\\\)</span> with <span>\\\\(p\\\\in [1,\\\\infty ]\\\\)</span>.</p></div>\",\"PeriodicalId\":649,\"journal\":{\"name\":\"Journal of Mathematical Fluid Mechanics\",\"volume\":\"26 4\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-10-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Fluid Mechanics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00021-024-00903-1\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-024-00903-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Ill-Posedness for the Cauchy Problem of the Modified Camassa-Holm Equation in \(B_{\infty ,1}^0\)
In this paper, we prove the norm inflation and get the ill-posedness for the modified Camassa-Holm equation in \(B_{\infty ,1}^0\). Therefore we completed all well-posedness and ill-posedness problem for the modified Camassa-Holm equation in all critical spaces \(B_{p,1}^\frac{1}{p}\) with \(p\in [1,\infty ]\).
期刊介绍：
The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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