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Viscous Shock Wave to an Inflow Problem for Compressible Viscous Gas with Large Density Oscillations
Bian, Dong-fen1; Fan, Li-li2; He, Lin3; Zhao, Hui-jiang4,5
2019
Source PublicationACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN0168-9673
Volume35Issue:1Pages:129-157
AbstractThis paper is concerned with the inflow problem for one-dimensional compressible Navier-Stokes equations. For such a problem, Huang, Matsumura, and Shi showed in [4] that there exists viscous shock wave solution to the inflow problem and both the boundary layer solution, the viscous shock wave, and their superposition are time-asymptotically nonlinear stable provided that both the initial perturbation and the boundary velocity are assumed to be sufficiently small. The main purpose of this paper is to show that similar stability results still hold for a class of large initial perturbation which can allow the initial density to have large oscillations. The proofs are given by an elementary energy method and our main idea is to use the smallness of the strength of the viscous shock wave and the boundary velocity to control the possible growth of the solutions induced by the nonlinearity of the compressible Navier-Stokes equations and the inflow boundary condition. The key point in our analysis is to deduce the desired uniform positive lower and upper bounds on the density.
Keywordcompressible Navier-Stokes equations inflow problem viscous shock wave large density oscillations
DOI10.1007/s10255-019-0801-2
Language英语
Funding ProjectNational Natural Science Foundation of China[11501028] ; National Natural Science Foundation of China[11871005] ; National Natural Science Foundation of China[11871388] ; National Natural Science Foundation of China[11671309] ; National Natural Science Foundation of China[11731008] ; China Postdoctoral Science Foundation[2015M570938] ; Fundamental Research Funds for the Central Universities
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000459979000006
PublisherSPRINGER HEIDELBERG
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34151
Collection中国科学院数学与系统科学研究院
Corresponding AuthorBian, Dong-fen
Affiliation1.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China
2.Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Hubei, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China
4.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China
5.Wuhan Univ, Computat Sci Hubei Key Lab, Wuhan 430072, Hubei, Peoples R China
Recommended Citation
GB/T 7714
Bian, Dong-fen,Fan, Li-li,He, Lin,et al. Viscous Shock Wave to an Inflow Problem for Compressible Viscous Gas with Large Density Oscillations[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2019,35(1):129-157.
APA Bian, Dong-fen,Fan, Li-li,He, Lin,&Zhao, Hui-jiang.(2019).Viscous Shock Wave to an Inflow Problem for Compressible Viscous Gas with Large Density Oscillations.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,35(1),129-157.
MLA Bian, Dong-fen,et al."Viscous Shock Wave to an Inflow Problem for Compressible Viscous Gas with Large Density Oscillations".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 35.1(2019):129-157.
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