{"title":"Properties of weak solutions to the Nordström–Vlasov system","authors":"Meixia Xiao","doi":"10.1063/5.0150177","DOIUrl":null,"url":null,"abstract":"In this article, we investigate the Nordström–Vlasov system in the whole space. The kinetic model is a relativistic generalization of the classical Vlasov–Poisson system in the gravitational case and describes the ensemble motion of collisionless particles interacting by means of a self-consistent scalar gravitational field. With the Fourier analysis and the smoothing effect of low velocity particles, we get a better regularity of weak solutions for the field than the one proved by Calogero and Rein [J. Differ. Equ. 204, 323 (2004)]. Meanwhile, under the additional integrability condition, we establish the energy conservation of the weak solution.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"214 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1063/5.0150177","RegionNum":3,"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 article, we investigate the Nordström–Vlasov system in the whole space. The kinetic model is a relativistic generalization of the classical Vlasov–Poisson system in the gravitational case and describes the ensemble motion of collisionless particles interacting by means of a self-consistent scalar gravitational field. With the Fourier analysis and the smoothing effect of low velocity particles, we get a better regularity of weak solutions for the field than the one proved by Calogero and Rein [J. Differ. Equ. 204, 323 (2004)]. Meanwhile, under the additional integrability condition, we establish the energy conservation of the weak solution.
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