{"title":"Generalized solutions to the model of compressible viscous fluids coupled with the Poisson equation","authors":"Zhong Tan, Hui Yang","doi":"10.1063/5.0190282","DOIUrl":null,"url":null,"abstract":"This paper deals with the model of compressible viscous and barotropic fluids coupled with the Poisson equation in a bounded domain Ω⊂R3 with C2+α (0 < α < 1) boundary ∂Ω. We prove the existence and weak-strong uniqueness of dissipative solutions when the adiabatic exponent γ > 1. We find that the Poisson term ρ∇Φ is not integrable when γ∈(1,32). We will make full use of the Poisson equation and energy inequality to overcome this difficulty. Finally, we obtain that ρ∇Φ leads to the decrease of Reynolds stress R and the increase of the energy dissipation defect E.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":"26 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-07-18","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/10.1063/5.0190282","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}
引用次数: 0
Abstract
This paper deals with the model of compressible viscous and barotropic fluids coupled with the Poisson equation in a bounded domain Ω⊂R3 with C2+α (0 < α < 1) boundary ∂Ω. We prove the existence and weak-strong uniqueness of dissipative solutions when the adiabatic exponent γ > 1. We find that the Poisson term ρ∇Φ is not integrable when γ∈(1,32). We will make full use of the Poisson equation and energy inequality to overcome this difficulty. Finally, we obtain that ρ∇Φ leads to the decrease of Reynolds stress R and the increase of the energy dissipation defect E.
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