Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data

doi:10.1007/s00220-015-2376-y

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	Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data
	Chen, Gui-Qiang G.1,2; Perepelitsa, Mikhail 3
	2015-09-01
发表期刊	COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN	0010-3616
卷号	338 期号:2 页码:771-800
摘要	We are concerned with spherically symmetric solutions of the Euler equations for multidimensional compressible fluids, which are motivated by many important physical situations. Various evidences indicate that spherically symmetric solutions of the compressible Euler equations may blow up near the origin at a certain time under some circumstance. The central feature is the strengthening of waves as they move radially inward. A longstanding open, fundamental problem is whether concentration could be formed at the origin. In this paper, we develop a method of vanishing viscosity and related estimate techniques for viscosity approximate solutions, and establish the convergence of the approximate solutions to a global finite-energy entropy solution of the isentropic Euler equations with spherical symmetry and large initial data. This indicates that concentration is not formed in the vanishing viscosity limit, even though the density may blow up at a certain time. To achieve this, we first construct global smooth solutions of appropriate initial-boundary value problems for the Euler equations with designed viscosity terms, approximate pressure function, and boundary conditions, and then we establish the strong convergence of the viscosity approximate solutions to a finite-energy entropy solution of the Euler equations.
DOI	10.1007/s00220-015-2376-y
语种	英语
资助项目	UK EPSRC Science and Innovation Award[EP/E035027/1] ; UK EPSRC Award[EP/L015811/1] ; NSFC[10728101] ; Royal Society-Wolfson Research Merit Award (UK) ; NSF[DMS-1108048] ; Isaac Newton Institute for Mathematical Sciences, Cambridge
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000357580400011
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20287
专题	中国科学院数学与系统科学研究院
通讯作者	Chen, Gui-Qiang G.
作者单位	1.Univ Oxford, Math Inst, Radcliffe Observ Quarter, Oxford OX2 6GG, England 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Houston, Dept Math, Houston, TX 77204 USA
推荐引用方式 GB/T 7714	Chen, Gui-Qiang G.,Perepelitsa, Mikhail. Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS,2015,338(2):771-800.
APA	Chen, Gui-Qiang G.,&Perepelitsa, Mikhail.(2015).Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data.COMMUNICATIONS IN MATHEMATICAL PHYSICS,338(2),771-800.
MLA	Chen, Gui-Qiang G.,et al."Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data".COMMUNICATIONS IN MATHEMATICAL PHYSICS 338.2(2015):771-800.