Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity

doi:10.1080/03605302.2010.516785

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	Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity
	Jiu, Quansen 1,2; Wang, Yi2,3,4 ; Xin, Zhouping 2
	2011
发表期刊	COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0360-5302
卷号	36 期号:4 页码:602-634
摘要	In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier-Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is constructed by approximating the system and regularizing the initial values which may contain vacuum states. Then some global in time estimates on the weak solution are obtained. Based on these uniform estimates, the vacuum states are shown to vanish in finite time and the weak solution we constructed becomes a unique strong one. Consequently, the stability of the rarefaction wave is proved in a weak sense. The theory holds for large-amplitudes rarefaction waves and arbitrary initial perturbations.
关键词	Density-dependent Navier-Stokes equations Rarefaction wave Stability Weak solution
DOI	10.1080/03605302.2010.516785
语种	英语
资助项目	National Natural Sciences Foundation of China[10871133] ; National Natural Sciences Foundation of China[10801128] ; Beijing Education Committee ; Zheng Ge Ru Funds ; Hong Kong RGC Earmarked Research Grant[CUHK4042/08P] ; Hong Kong RGC Earmarked Research Grant[CUHK4040/06P] ; Chinese University of Hong Kong
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000286522000002
出版者	TAYLOR & FRANCIS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13059
专题	应用数学研究所
通讯作者	Jiu, Quansen
作者单位	1.Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China 2.Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China 3.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing, Peoples R China 4.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Jiu, Quansen,Wang, Yi,Xin, Zhouping. Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,2011,36(4):602-634.
APA	Jiu, Quansen,Wang, Yi,&Xin, Zhouping.(2011).Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity.COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,36(4),602-634.
MLA	Jiu, Quansen,et al."Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity".COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 36.4(2011):602-634.