{"title":"Asymptotic analysis for 1D compressible Navier-Stokes-Vlasov equations","authors":"Xinran Shi, Yunfei Su, Lei Yao","doi":"10.3934/cpaa.2020119","DOIUrl":null,"url":null,"abstract":"We consider the initial-boundary value problem of compressible Navier–Stokes–Vlasov equations under a local alignment regime in a one-dimensional bounded domain. Based on the relative entropy method and compactness argument, we prove that a weak solution of the initial-boundary value problem converges to a strong solution of the limiting two-phase fluid system. This work extends in some sense the previous work of Choi and Jung [Math. Models Methods Appl. Sci. 31(11), 2213–2295 (2021)], which considered the diffusive term ∂ ξξ f ɛ in the kinetic equation. Note that the diffusion term was not considered in this paper.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"37 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Pure and Applied Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/cpaa.2020119","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
We consider the initial-boundary value problem of compressible Navier–Stokes–Vlasov equations under a local alignment regime in a one-dimensional bounded domain. Based on the relative entropy method and compactness argument, we prove that a weak solution of the initial-boundary value problem converges to a strong solution of the limiting two-phase fluid system. This work extends in some sense the previous work of Choi and Jung [Math. Models Methods Appl. Sci. 31(11), 2213–2295 (2021)], which considered the diffusive term ∂ ξξ f ɛ in the kinetic equation. Note that the diffusion term was not considered in this paper.
研究一维有界区域上局部对准区域下可压缩Navier-Stokes-Vlasov方程的初边值问题。基于相对熵法和紧性论证，证明了初始边值问题的弱解收敛于极限两相流体系统的强解。这项工作在某种意义上扩展了Choi和Jung之前的工作。模型、方法、应用。科学通报，31(11)，2213-2295(2021)]，考虑了动力学方程中的扩散项∂ξξ f /。请注意，本文没有考虑扩散项。
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CPAA publishes original research papers of the highest quality in all the major areas of analysis and its applications, with a central theme on theoretical and numeric differential equations. Invited expository articles are also published from time to time. It is edited by a group of energetic leaders to guarantee the journal''s highest standard and closest link to the scientific communities.
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