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UNIFORM REGULARITY AND VANISHING VISCOSITY LIMIT FOR THE COMPRESSIBLE NAVIER-STOKES WITH GENERAL NAVIER-SLIP BOUNDARY CONDITIONS IN THREE-DIMENSIONAL DOMAINS
Wang, Yong1; Xin, Zhouping2; Yong, Yan3
2015
Source PublicationSIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN0036-1410
Volume47Issue:6Pages:4123-4191
AbstractIn this paper, we investigate the uniform regularity for the isentropic compressible Navier-Stokes system with general Navier-slip boundary conditions (1.6) and the inviscid limit to the compressible Euler system. It is shown that there exists a unique strong solution of the compressible Navier-Stokes equations with general Navier-slip boundary conditions in an interval of time which is uniform in the vanishing viscosity limit. The solution is uniformly bounded in a conormal Sobolev space and is uniformly bounded in W-1,W-infinity. It is also shown that the boundary layer for the density is weaker than the one for the velocity field. In particular, it is proved that the velocity will be uniformly bounded in L-infinity(0, T; H-2) when the boundary is flat and the Navier-Stokes system is supplemented with the vorticity free boundary condition (1.25). Based on such uniform estimates, we prove the convergence of the viscous solutions to the inviscid ones in L-infinity(0, T; L-2), L-infinity(0, T; H-1) and L-infinity([0, T] x Omega) with a rate of convergence.
Keywordcompressible Navier-Stokes Euler equations vanishing viscosity limit convergence rate
DOI10.1137/151003520
Language英语
Funding ProjectZheng Ge Ru Foundation ; Hong Kong RGC Earmarked Research grant[CUHK4041/11P] ; Hong Kong RGC Earmarked Research grant[CUHK4048/13P] ; NSFC/RGC Joint Research Scheme grant[N-CUHK443/14] ; Croucher Foundation ; Focus Area grant at The Chinese University of Hong Kong ; National Natural Sciences Foundation of China[11371064] ; National Natural Sciences Foundation of China[11401565] ; National Natural Sciences Foundation of China[11201301] ; Hujiang Foundation of China[B14005]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000367020000002
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21586
Collection应用数学研究所
Affiliation1.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China
2.Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China
3.Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China
Recommended Citation
GB/T 7714
Wang, Yong,Xin, Zhouping,Yong, Yan. UNIFORM REGULARITY AND VANISHING VISCOSITY LIMIT FOR THE COMPRESSIBLE NAVIER-STOKES WITH GENERAL NAVIER-SLIP BOUNDARY CONDITIONS IN THREE-DIMENSIONAL DOMAINS[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2015,47(6):4123-4191.
APA Wang, Yong,Xin, Zhouping,&Yong, Yan.(2015).UNIFORM REGULARITY AND VANISHING VISCOSITY LIMIT FOR THE COMPRESSIBLE NAVIER-STOKES WITH GENERAL NAVIER-SLIP BOUNDARY CONDITIONS IN THREE-DIMENSIONAL DOMAINS.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,47(6),4123-4191.
MLA Wang, Yong,et al."UNIFORM REGULARITY AND VANISHING VISCOSITY LIMIT FOR THE COMPRESSIBLE NAVIER-STOKES WITH GENERAL NAVIER-SLIP BOUNDARY CONDITIONS IN THREE-DIMENSIONAL DOMAINS".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 47.6(2015):4123-4191.
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