{"title":"Global Existence Theorem of Mild Solutions of the Boltzmann Equation for Short Range Interactions","authors":"Emmanuel Kamdem Tchtjengtje, Etienne Takou","doi":"10.1016/S0034-4877(22)00079-9","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation<span> with near vacuum initial data where the distribution function depends on time, position and momenta. The collision kernel considered here corresponds to short range interactions and the background space-time is fixed and is of Bianchi type I. The existence of a unique global (in time) mild solution is obtained in a suitable weighted space.</span></p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"90 3","pages":"Pages 325-345"},"PeriodicalIF":1.0000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487722000799","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
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Abstract
In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data where the distribution function depends on time, position and momenta. The collision kernel considered here corresponds to short range interactions and the background space-time is fixed and is of Bianchi type I. The existence of a unique global (in time) mild solution is obtained in a suitable weighted space.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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