{"title":"A Remark about Time-Analyticity of the Linear Landau Equation with Soft Potential","authors":"Chaojiang Xu, Yan Xu","doi":"10.4208/ata.oa-2022-0029","DOIUrl":null,"url":null,"abstract":"In this note, we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials. We prove that the solution to the Cauchy\nproblem enjoys the analytic regularizing effect of the time variable with an $L^2$ initial\ndatum for positive time. So that the smoothing effect of Cauchy problem for the linear spatially homogeneous Landau equation with soft potentials is similar to the heat\nequation.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"103 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis in Theory and Applications","FirstCategoryId":"95","ListUrlMain":"https://doi.org/10.4208/ata.oa-2022-0029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this note, we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials. We prove that the solution to the Cauchy
problem enjoys the analytic regularizing effect of the time variable with an $L^2$ initial
datum for positive time. So that the smoothing effect of Cauchy problem for the linear spatially homogeneous Landau equation with soft potentials is similar to the heat
equation.
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