{"title":"Existence and Smoothing Effect of Measure Valued Solution to the Homogeneous Boltzmann Equation with Debye–Yukawa Potential","authors":"Shuaikun Wang, Tong Yang","doi":"10.1137/23m1562123","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 5969-5994, October 2024. <br/> Abstract. In this paper, we consider the measure valued solution to the homogeneous Boltzmann equation with Debye–Yukawa potential. First, for the case of the true Debye–Yukawa potential, we prove global in time existence of a solution with properties such as gain of moments. And then we consider the Maxwellian molecule of Deybe–Yukawa type potential. By introducing a new coercivity estimate, we show that the solution [math] for any [math], as long as the initial data [math] is not orthogonal to two translations of the measure itself.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1562123","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 5969-5994, October 2024. Abstract. In this paper, we consider the measure valued solution to the homogeneous Boltzmann equation with Debye–Yukawa potential. First, for the case of the true Debye–Yukawa potential, we prove global in time existence of a solution with properties such as gain of moments. And then we consider the Maxwellian molecule of Deybe–Yukawa type potential. By introducing a new coercivity estimate, we show that the solution [math] for any [math], as long as the initial data [math] is not orthogonal to two translations of the measure itself.
期刊介绍：
SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena.
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Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.
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