Global entropy solutions to multi-dimensional isentropic gas dynamics with spherical symmetry

doi:10.1088/1361-6544/ab31ce

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	Global entropy solutions to multi-dimensional isentropic gas dynamics with spherical symmetry
	Huang, Feimin 1,3; Li, Tianhong 3; Yuan, Difan 1,2
刊名	NONLINEARITY
	2019-11-01
卷号	32 期号:11 页码:4505-4523
关键词	isentropic gas compensated compactness uniform estimate
ISSN号	0951-7715
DOI	10.1088/1361-6544/ab31ce
英文摘要	We are concerned with spherically symmetric solutions to Euler equations for multi-dimensional compressible fluids which have many applications in diverse real physical situations. The system can be reduced to one-dimensional isentropic gas dynamics with geometric source terms. Due to the presence of the singularity at the origin, there are few papers devoted to this problem. The present paper proves two existence theorems of global entropy solutions. The first one focuses on a case excluding the origin in which negative velocity is allowed, and the second one corresponds to a case which includes the origin with non-negative velocity. The L-infinity compensated compactness framework and vanishing viscosity method are applied to prove the convergence of approximate solutions. In the second case, we show that if the blast wave initially moves outwards and the initial densities and velocities decay to zero with certain rates near the origin, then the densities and velocities tend to zero with the same rates near the origin for any positive time. In particular, the entropy solutions in two existence theorems are uniformly bounded with respect to time.
资助项目	National Center for Mathematics and Interdisciplinary Sciences, AMSS, CAS ; NSFC[11371349] ; NSFC[11688101] ; National Natural Science Foundation of China[10931007] ; National Natural Science Foundation of China[11771429] ; China Scholarship Council[201704910503]
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	IOP PUBLISHING LTD
WOS记录号	WOS:000518794400012
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50922]
专题	数学所
通讯作者	Yuan, Difan
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Chinese Acad Sci, AMSS, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Huang, Feimin,Li, Tianhong,Yuan, Difan. Global entropy solutions to multi-dimensional isentropic gas dynamics with spherical symmetry[J]. NONLINEARITY,2019,32(11):4505-4523.
APA	Huang, Feimin,Li, Tianhong,&Yuan, Difan.(2019).Global entropy solutions to multi-dimensional isentropic gas dynamics with spherical symmetry.NONLINEARITY,32(11),4505-4523.
MLA	Huang, Feimin,et al."Global entropy solutions to multi-dimensional isentropic gas dynamics with spherical symmetry".NONLINEARITY 32.11(2019):4505-4523.