KMS Of Academy of mathematics and systems sciences, CAS
Global entropy solutions to multi-dimensional isentropic gas dynamics with spherical symmetry | |
Huang, Feimin1,2; Li, Tianhong2; Yuan, Difan1,3 | |
2019-11-01 | |
Source Publication | NONLINEARITY |
ISSN | 0951-7715 |
Volume | 32Issue:11Pages:4505-4523 |
Abstract | 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. |
Keyword | isentropic gas compensated compactness uniform estimate |
DOI | 10.1088/1361-6544/ab31ce |
Indexed By | SCI |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics ; Physics |
WOS Subject | Mathematics, Applied ; Physics, Mathematical |
WOS ID | WOS:000518794400012 |
Publisher | IOP PUBLISHING LTD |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50923 |
Collection | 应用数学研究所 数学所 |
Corresponding Author | Yuan, Difan |
Affiliation | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, AMSS, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
Recommended Citation 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. |
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