Uniform regularity for the free surface compressible Navier-Stokes equations with or without surface tension

doi:10.1142/S0218202518500082

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	Uniform regularity for the free surface compressible Navier-Stokes equations with or without surface tension
	Mei, Yu 1; Wang, Yong2 ; Xin, Zhouping 3
	2018-02-01
发表期刊	MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
ISSN	0218-2025
卷号	28 期号:2 页码:259-336
摘要	In 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.
关键词	Vanishing viscosity surface tension free surface compressible Navier-Stokes
DOI	10.1142/S0218202518500082
语种	英语
资助项目	National 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研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000418859000003
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/27036
专题	应用数学研究所
通讯作者	Mei, Yu
作者单位	1.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
推荐引用方式 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.