{"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}
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.