Kramers-Fokker-Planck方程解的全局时间$L^p−L^q$估计

数学研究通讯 Pub Date : 2021-07-07 DOI:10.4208/cmr.2021-0081

Xue Ping Wang, Lu Zhu

{"title":"Kramers-Fokker-Planck方程解的全局时间$L^p−L^q$估计","authors":"Xue Ping Wang, Lu Zhu","doi":"10.4208/cmr.2021-0081","DOIUrl":null,"url":null,"abstract":"In this work, we prove an optimal global-in-time Lp−Lq estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension three. Our result shows that the decay rate as t → +∞ is the same as the heat equation in x-variables and the divergence rate as t → 0+ is related to the sub-ellipticity with loss of 1/3 derivatives of the Kramers-Fokker-Planck operator.","PeriodicalId":66427,"journal":{"name":"数学研究通讯","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Global-in-Time $L^p−L^q$ Estimates for Solutions of the Kramers-Fokker-Planck Equation\",\"authors\":\"Xue Ping Wang, Lu Zhu\",\"doi\":\"10.4208/cmr.2021-0081\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we prove an optimal global-in-time Lp−Lq estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension three. Our result shows that the decay rate as t → +∞ is the same as the heat equation in x-variables and the divergence rate as t → 0+ is related to the sub-ellipticity with loss of 1/3 derivatives of the Kramers-Fokker-Planck operator.\",\"PeriodicalId\":66427,\"journal\":{\"name\":\"数学研究通讯\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"数学研究通讯\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4208/cmr.2021-0081\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究通讯","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4208/cmr.2021-0081","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 2

摘要

在这项工作中，我们证明了三维具有短程势的Kramers-Fokker-Planck方程解的最优全局时间Lp−Lq估计。我们的结果表明→ +∞ 与x变量中的热方程相同，发散率为t→ 0+与Kramers-Fokker-Planck算子的1/3导数损失的亚椭圆率有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Global-in-Time $L^p−L^q$ Estimates for Solutions of the Kramers-Fokker-Planck Equation

In this work, we prove an optimal global-in-time Lp−Lq estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension three. Our result shows that the decay rate as t → +∞ is the same as the heat equation in x-variables and the divergence rate as t → 0+ is related to the sub-ellipticity with loss of 1/3 derivatives of the Kramers-Fokker-Planck operator.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

数学研究通讯

自引率

0.00%

发文量

1035