{"title":"具有软势能的玻尔兹曼方程的良好/全拟合性","authors":"Xuwen Chen, Shunlin Shen, Zhifei Zhang","doi":"10.1007/s00220-024-05157-6","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-posedness in <span>\\(H^{s}\\)</span> Sobolev space. We find the well/ill-posedness separation at regularity <span>\\(s=\\frac{d-1}{2}\\)</span>, strictly <span>\\(\\frac{1}{2}\\)</span>-derivative higher than the scaling-invariant index <span>\\(s=\\frac{d-2}{2}\\)</span>, the usually expected separation point.\n</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 12","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Well/Ill-Posedness of the Boltzmann Equation with Soft Potential\",\"authors\":\"Xuwen Chen, Shunlin Shen, Zhifei Zhang\",\"doi\":\"10.1007/s00220-024-05157-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-posedness in <span>\\\\(H^{s}\\\\)</span> Sobolev space. We find the well/ill-posedness separation at regularity <span>\\\\(s=\\\\frac{d-1}{2}\\\\)</span>, strictly <span>\\\\(\\\\frac{1}{2}\\\\)</span>-derivative higher than the scaling-invariant index <span>\\\\(s=\\\\frac{d-2}{2}\\\\)</span>, the usually expected separation point.\\n</p></div>\",\"PeriodicalId\":522,\"journal\":{\"name\":\"Communications in Mathematical Physics\",\"volume\":\"405 12\",\"pages\":\"\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-11-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00220-024-05157-6\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s00220-024-05157-6","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Well/Ill-Posedness of the Boltzmann Equation with Soft Potential
We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-posedness in \(H^{s}\) Sobolev space. We find the well/ill-posedness separation at regularity \(s=\frac{d-1}{2}\), strictly \(\frac{1}{2}\)-derivative higher than the scaling-invariant index \(s=\frac{d-2}{2}\), the usually expected separation point.
期刊介绍：
The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
