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THE INVISCID LIMIT TO A CONTACT DISCONTINUITY FOR THE COMPRESSIBLE NAVIER-STOKES-FOURIER SYSTEM USING THE RELATIVE ENTROPY METHOD
Vasseur, Alexis1; Wang, Yi2,3
2015
Source PublicationSIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN0036-1410
Volume47Issue:6Pages:4350-4359
AbstractWe consider the zero heat conductivity limit to a contact discontinuity for the mono-dimensional full compressible Navier-Stokes-Fourier system. The method is based on the relative entropy method and does not assume any smallness conditions on the discontinuity nor on the bounded variation norm of the initial data. It is proved that for any viscosity v >= 0, the solution of the compressible Navier-Stokes-Fourier system (with well-prepared initial value) converges, when the heat conductivity kappa tends to zero, to the contact discontinuity solution to the corresponding Euler system. We obtain the decay rate kappa(1/2). It implies that the heat conductivity dominates the dissipation in the regime of the limit to a contact discontinuity. This is the first result, based on the relative entropy, of an asymptotic limit to a discontinuous solution for a system.
Keywordcontact discontinuity inviscid limit compressible Navier-Stokes-Fourier system relative entropy method
DOI10.1137/15M1023439
Language英语
Funding ProjectNSF[DMS 1209420] ; NSFC[11171326] ; NSFC[11322106] ; Youth Innovation Promotion Association, CAS
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000367020000008
PublisherSIAM PUBLICATIONS
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21562
Collection应用数学研究所
Affiliation1.Univ Texas Austin, Dept Math, Austin, TX 78712 USA
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Beijing Ctr Math & Informat Sci, Beijing 100048, Peoples R China
Recommended Citation
GB/T 7714
Vasseur, Alexis,Wang, Yi. THE INVISCID LIMIT TO A CONTACT DISCONTINUITY FOR THE COMPRESSIBLE NAVIER-STOKES-FOURIER SYSTEM USING THE RELATIVE ENTROPY METHOD[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2015,47(6):4350-4359.
APA Vasseur, Alexis,&Wang, Yi.(2015).THE INVISCID LIMIT TO A CONTACT DISCONTINUITY FOR THE COMPRESSIBLE NAVIER-STOKES-FOURIER SYSTEM USING THE RELATIVE ENTROPY METHOD.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,47(6),4350-4359.
MLA Vasseur, Alexis,et al."THE INVISCID LIMIT TO A CONTACT DISCONTINUITY FOR THE COMPRESSIBLE NAVIER-STOKES-FOURIER SYSTEM USING THE RELATIVE ENTROPY METHOD".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 47.6(2015):4350-4359.
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