{"title":"The analytic Gelfand-Shilov smoothing effect of the Landau equation with hard potential","authors":"Chao-Jiang Xu, Yan Xu","doi":"10.1016/j.jde.2024.09.019","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study the Cauchy problem of the inhomogeneous Landau equation with hard potentials under the perturbation framework to global equilibrium. We prove that the solution to the Cauchy problem enjoys the analytic Gelfand-Shilov regularizing effect with a Sobolev initial datum for positive time.</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"414 ","pages":"Pages 645-681"},"PeriodicalIF":2.4000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039624005990","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the Cauchy problem of the inhomogeneous Landau equation with hard potentials under the perturbation framework to global equilibrium. We prove that the solution to the Cauchy problem enjoys the analytic Gelfand-Shilov regularizing effect with a Sobolev initial datum for positive time.
期刊介绍：
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics
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