Global existence proof for the spatially homogeneous relativistic Boltzmann equation with soft potentials

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Applicable Analysis Pub Date : 2023-10-11 DOI:10.1080/00036811.2023.2260406

Jianjun Huang, Zhenglu Jiang

{"title":"Global existence proof for the spatially homogeneous relativistic Boltzmann equation with soft potentials","authors":"Jianjun Huang, Zhenglu Jiang","doi":"10.1080/00036811.2023.2260406","DOIUrl":null,"url":null,"abstract":"AbstractWe study the spatially homogeneous solutions for the relativistic kinetic equations. It is shown that the Cauchy problem for the relativistic Boltzmann and Landau equation with soft potentials admits a global weak solution if the mass, energy and entropy of the initial data are finite. Besides the asymptotic behavior of grazing collisions of the relativistic Boltzmann equation is concerned. We prove that the subsequences of solutions to the relativistic Boltzmann equation weakly converge to the solutions of the relativistic Landau equation when almost all the collisions are grazing. These results are extensions of the work of Villani for the spatially homogeneous Boltzmann and Landau equations in the classical case.Keywords: Relativistic Boltzmann equationrelativistic Landau equationsoft potentialsgrazing collision2010 Mathematics Subject Classification: 35Q20 AcknowledgementsThe authors would like to thank the referees of this paper for their helpful suggestions on this work.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by NSFC 11171356.","PeriodicalId":55507,"journal":{"name":"Applicable Analysis","volume":"43 1","pages":"0"},"PeriodicalIF":1.1000,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00036811.2023.2260406","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

AbstractWe study the spatially homogeneous solutions for the relativistic kinetic equations. It is shown that the Cauchy problem for the relativistic Boltzmann and Landau equation with soft potentials admits a global weak solution if the mass, energy and entropy of the initial data are finite. Besides the asymptotic behavior of grazing collisions of the relativistic Boltzmann equation is concerned. We prove that the subsequences of solutions to the relativistic Boltzmann equation weakly converge to the solutions of the relativistic Landau equation when almost all the collisions are grazing. These results are extensions of the work of Villani for the spatially homogeneous Boltzmann and Landau equations in the classical case.Keywords: Relativistic Boltzmann equationrelativistic Landau equationsoft potentialsgrazing collision2010 Mathematics Subject Classification: 35Q20 AcknowledgementsThe authors would like to thank the referees of this paper for their helpful suggestions on this work.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by NSFC 11171356.

查看原文本刊更多论文

具有软势的空间齐次相对论玻尔兹曼方程的整体存在性证明

摘要研究了相对论性动力学方程的空间齐次解。在初始数据的质量、能量和熵有限的情况下，证明了具有软势的相对论性Boltzmann - Landau方程的Cauchy问题存在全局弱解。此外，还讨论了相对论玻尔兹曼方程的掠掠碰撞的渐近行为。证明了当几乎所有碰撞都是掠射时，相对论性玻尔兹曼方程解的子序列弱收敛于相对论性朗道方程的解。这些结果是维拉尼在经典情况下对空间齐次玻尔兹曼方程和朗道方程的工作的扩展。关键词:相对论玻尔兹曼方程相对论朗道方程软势擦碰2010数学学科分类:35Q20致谢感谢本文审稿人对本文工作提出的有益建议。披露声明作者未报告潜在的利益冲突。本研究得到国家自然科学基金11171356资助。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applicable Analysis 数学-应用数学

CiteScore

2.60

自引率

9.10%

发文量

175

审稿时长

2 months

期刊介绍： Applicable Analysis is concerned primarily with analysis that has application to scientific and engineering problems. Papers should indicate clearly an application of the mathematics involved. On the other hand, papers that are primarily concerned with modeling rather than analysis are outside the scope of the journal General areas of analysis that are welcomed contain the areas of differential equations, with emphasis on PDEs, and integral equations, nonlinear analysis, applied functional analysis, theoretical numerical analysis and approximation theory. Areas of application, for instance, include the use of homogenization theory for electromagnetic phenomena, acoustic vibrations and other problems with multiple space and time scales, inverse problems for medical imaging and geophysics, variational methods for moving boundary problems, convex analysis for theoretical mechanics and analytical methods for spatial bio-mathematical models.