Vanishing Viscosity Solutions of the Compressible Euler Equations with Spherical Symmetry and Large Initial Data
文献类型：期刊论文
| 作者 | Chen, Gui-Qiang G.1,2; Perepelitsa, Mikhail3 |
| 刊名 | COMMUNICATIONS IN MATHEMATICAL PHYSICS
 |
| 出版日期 | 2015-09-01 |
| 卷号 | 338期号:2页码:771-800 |
| ISSN号 | 0010-3616 |
| DOI | 10.1007/s00220-015-2376-y |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| 出版者 | SPRINGER |
| WOS记录号 | WOS:000357580400011 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/20286]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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