Weak Continuity and Compactness for Nonlinear Partial Differential Equations
文献类型：期刊论文
| 作者 | Chen, Gui-Qiang G.1,2,3 |
| 刊名 | CHINESE ANNALS OF MATHEMATICS SERIES B
 |
| 出版日期 | 2015-09-01 |
| 卷号 | 36期号:5页码:715-736 |
| 关键词 | Weak continuity Compensated compactness Nonlinear partial differential equations Euler equations Gauss-Codazzi-Ricci system |
| ISSN号 | 0252-9599 |
| DOI | 10.1007/s11401-015-0973-x |
| 英文摘要 | This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. The compactness and convergence of vanishing viscosity solutions for nonlinear hyperbolic conservation laws are first analyzed, including the inviscid limit from the Navier-Stokes equations to the Euler equations for homentropic flow, the vanishing viscosity method to construct the global spherically symmetric solutions to the multidimensional compressible Euler equations, and the sonic-subsonic limit of solutions of the full Euler equations for multi-dimensional steady compressible fluids. Then the weak continuity and rigidity of the Gauss-Codazzi-Ricci system and corresponding isometric embeddings in differential geometry are revealed. Further references are also provided for some recent developments on the weak continuity and compactness for nonlinear partial differential equations. |
| 语种 | 英语 |
| WOS记录号 | WOS:000360569000005 |
| 出版者 | SHANGHAI SCIENTIFIC TECHNOLOGY LITERATURE PUBLISHING HOUSE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/20715]  |
| 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.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Oxford, Math Inst, Oxford OX2 6GG, England |
| 推荐引用方式 GB/T 7714 | Chen, Gui-Qiang G.. Weak Continuity and Compactness for Nonlinear Partial Differential Equations[J]. CHINESE ANNALS OF MATHEMATICS SERIES B,2015,36(5):715-736. |
| APA | Chen, Gui-Qiang G..(2015).Weak Continuity and Compactness for Nonlinear Partial Differential Equations.CHINESE ANNALS OF MATHEMATICS SERIES B,36(5),715-736. |
| MLA | Chen, Gui-Qiang G.."Weak Continuity and Compactness for Nonlinear Partial Differential Equations".CHINESE ANNALS OF MATHEMATICS SERIES B 36.5(2015):715-736. |
入库方式： OAI收割
来源：数学与系统科学研究院
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