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Uniform regularity for the free surface compressible Navier-Stokes equations with or without surface tension
Mei, Yu1; Wang, Yong2; Xin, Zhouping3
2018-02-01
Source PublicationMATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
ISSN0218-2025
Volume28Issue:2Pages:259-336
AbstractIn this paper, we investigate the uniform regularity of solutions to the three-dimensional isentropic compressible Navier-Stokes system with free surfaces and study the corresponding asymptotic limits of such solutions to that of the compressible Euler system for vanishing viscosity and surface tension. It is shown that there exists a unique strong solution to the free boundary problem for the compressible Navier-Stokes system in a finite time interval which is independent of the viscosity and the surface tension. The solution is uniformly bounded both in W-1,W-infinity and a conormal Sobolev space. It is also shown that the boundary layer for the density is weaker than the one for the velocity field. Based on such uniform estimates, the asymptotic limits, to the free boundary problem for the ideal compressible Euler system with or without surface tension as both the viscosity and the surface tension tend to zero, are established by a strong convergence argument.
KeywordVanishing viscosity surface tension free surface compressible Navier-Stokes
DOI10.1142/S0218202518500082
Language英语
Funding ProjectNational Natural Sciences Foundation of China[11401565] ; National Natural Sciences Foundation of China[11688101] ; Zheng Ge Ru Funds ; Hong Kong RGC Earmarked Research Grants[CUHK4041/11P] ; Hong Kong RGC Earmarked Research Grants[CUHK4048/13P] ; NSFC/RGC Joint Research Scheme Grant[CUHK443/14] ; Croucher Foundation ; Focus Area Grant at the Chinese University of Hong Kong
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000418859000003
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/27036
Collection应用数学研究所
Affiliation1.Chinese Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China
2.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China
3.Chinese Univ Hong Kong, Inst Math Sci, Hong Kong, Hong Kong, Peoples R China
Recommended Citation
GB/T 7714
Mei, Yu,Wang, Yong,Xin, Zhouping. Uniform regularity for the free surface compressible Navier-Stokes equations with or without surface tension[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES,2018,28(2):259-336.
APA Mei, Yu,Wang, Yong,&Xin, Zhouping.(2018).Uniform regularity for the free surface compressible Navier-Stokes equations with or without surface tension.MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES,28(2),259-336.
MLA Mei, Yu,et al."Uniform regularity for the free surface compressible Navier-Stokes equations with or without surface tension".MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES 28.2(2018):259-336.
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