{"title":"The Euler Limit of the Relativistic Boltzmann Equation","authors":"Dongcheng Yang and Hongjun Yu","doi":"10.4208/cmaa.2023-0001","DOIUrl":"https://doi.org/10.4208/cmaa.2023-0001","url":null,"abstract":"In this work we prove the existence and uniqueness theorems of the solutions to the relativistic Boltzmann equation for analytic initial fluctuations on a time interval independent of the Knudsen number ǫ > 0. As ǫ → 0, we prove that the solution of the relativistic Boltzmann equation tends to the local relativistic Maxwellian, whose fluid-dynamical parameters solve the relativistic Euler equations and the convergence rate is also obtained. Due to this convergence rate, the Hilbert expansion is verified in the short time interval for the relativistic Boltzmann equation. We also consider the physically important initial layer problem. As a by-product, an existence theorem for the relativistic Euler equations without the assumption of the non-vacuum fluid states is obtained. AMS subject classifications: 35Q99, 82A47","PeriodicalId":371957,"journal":{"name":"Communications in Mathematical Analysis and Applications","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122487786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Decay of the Compressible Navier-Stokes Equations with Hyperbolic Heat Conduction","authors":"Zhigang Wu, Wenyue Li","doi":"10.4208/cmaa.2022-0022","DOIUrl":"https://doi.org/10.4208/cmaa.2022-0022","url":null,"abstract":"","PeriodicalId":371957,"journal":{"name":"Communications in Mathematical Analysis and Applications","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129498865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Brachistochrone Problem","authors":"P. G. Ciarlet, C. Mardare","doi":"10.4208/cmaa.2021-0005","DOIUrl":"https://doi.org/10.4208/cmaa.2021-0005","url":null,"abstract":"","PeriodicalId":371957,"journal":{"name":"Communications in Mathematical Analysis and Applications","volume":"218 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115522447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Self-Similar Solutions of Leray’s Type for Compressible Navier-Stokes Equations in Two Dimension","authors":"Xianpeng Hu","doi":"10.4208/cmaa.2022-0001","DOIUrl":"https://doi.org/10.4208/cmaa.2022-0001","url":null,"abstract":"","PeriodicalId":371957,"journal":{"name":"Communications in Mathematical Analysis and Applications","volume":"246 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122062408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Boundedness and Asymptotic Stability in a Chemotaxis Model with Signal-Dependent Motility and Nonlinear Signal Secretion","authors":"Xinyu Tu, Chunlai Mu, Shuyan Qiu null, Jing Zhang","doi":"10.4208/cmaa.2022-0018","DOIUrl":"https://doi.org/10.4208/cmaa.2022-0018","url":null,"abstract":"","PeriodicalId":371957,"journal":{"name":"Communications in Mathematical Analysis and Applications","volume":"212 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115974116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal Decay Rates of Solutions to a Blood Flow Model","authors":"Minyi Guo, Nangao Zhang, Changjiang Zhu","doi":"10.4208/cmaa.2022-0016","DOIUrl":"https://doi.org/10.4208/cmaa.2022-0016","url":null,"abstract":"","PeriodicalId":371957,"journal":{"name":"Communications in Mathematical Analysis and Applications","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116846146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Asymptotic Behavior of Solutions to One-Dimensional Compressible Navier-Stokes-Poisson Equations with Large Initial Data","authors":"Lan Zhang, Huijiang Zhao null, Qingsong Zhao","doi":"10.4208/cmaa.2022-0002","DOIUrl":"https://doi.org/10.4208/cmaa.2022-0002","url":null,"abstract":"","PeriodicalId":371957,"journal":{"name":"Communications in Mathematical Analysis and Applications","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124928829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Intrinsic Formulation of the Kirchhoff-Love Theory of Nonlinearly Elastic Shallow Shells","authors":"P. G. Ciarlet, C. Mardare","doi":"10.4208/cmaa.2022-0017","DOIUrl":"https://doi.org/10.4208/cmaa.2022-0017","url":null,"abstract":"","PeriodicalId":371957,"journal":{"name":"Communications in Mathematical Analysis and Applications","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121831250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On a New Type of Chemotaxis Model with Acceleration","authors":"Weirun Tao null, Zhian Wang","doi":"10.4208/cmaa.2022-0003","DOIUrl":"https://doi.org/10.4208/cmaa.2022-0003","url":null,"abstract":"","PeriodicalId":371957,"journal":{"name":"Communications in Mathematical Analysis and Applications","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116971209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On Short Wave-Long Wave Interactions in the Relativistic Context","authors":"João Paulo Dias null, H. Frid","doi":"10.4208/cmaa.2021-0006","DOIUrl":"https://doi.org/10.4208/cmaa.2021-0006","url":null,"abstract":"","PeriodicalId":371957,"journal":{"name":"Communications in Mathematical Analysis and Applications","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128618245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}