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Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional full compressible Navier-Stokes equations
Li, Xing1; Li, Lin-An2,3
2020-08-05
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume269Issue:4Pages:3160-3195
AbstractThe vanishing viscosity limit for the multi-dimensional compressible Navier-Stokes equations to the corresponding Euler equations is a difficult and challenging problem in the mathematics. Recently, L.Li, D.Wang and Y.Wang [17] verified that the solutions for the 2D compressible isentropic Navier-Stokes equations converge to the planar rarefaction wave solution for the corresponding 2D Euler equations as viscosity vanishes with a convergence rate epsilon(1/6) vertical bar ln epsilon vertical bar. In this paper, the vanishing viscosity limit of 2D non-isentropic compressible Navier-Stokes equations is studied. In contrast to the work [17], the convergence rate for the 2D full compressible Navier-Stokes equations is improved to epsilon(2/7) vertical bar ln epsilon vertical bar(2) by choosing a different scaling argument and performing more detailed energy estimates. (C) 2020 Elsevier Inc. All rights reserved.
KeywordEuler equations Planar rarefaction wave Hyperbolic wave Vanishing viscosity Navier-Stokes equations
DOI10.1016/j.jde.2020.02.026
Indexed BySCI
Language英语
Funding ProjectNSFC[11971320]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000534488300015
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/51498
Collection中国科学院数学与系统科学研究院
Corresponding AuthorLi, Lin-An
Affiliation1.Shenzhen Univ, Coll Math & Stat, Shenzhen 518060, Peoples R China
2.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Li, Xing,Li, Lin-An. Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional full compressible Navier-Stokes equations[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2020,269(4):3160-3195.
APA Li, Xing,&Li, Lin-An.(2020).Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional full compressible Navier-Stokes equations.JOURNAL OF DIFFERENTIAL EQUATIONS,269(4),3160-3195.
MLA Li, Xing,et al."Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional full compressible Navier-Stokes equations".JOURNAL OF DIFFERENTIAL EQUATIONS 269.4(2020):3160-3195.
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