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

doi:10.1080/03605302.2010.516785

	Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity
	Jiu, Quansen 1,2; Wang, Yi 2,3,4; Xin, Zhouping 2
刊名	COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
	2011
卷号	36 期号:4 页码:602-634
关键词	Density-dependent Navier-Stokes equations Rarefaction wave Stability Weak solution
ISSN号	0360-5302
DOI	10.1080/03605302.2010.516785
英文摘要	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.
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
语种	英语
出版者	TAYLOR & FRANCIS INC
WOS记录号	WOS:000286522000002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/13058]
专题	中国科学院数学与系统科学研究院
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.