KMS Of Academy of mathematics and systems sciences, CAS
| Weak Continuity and Compactness for Nonlinear Partial Differential Equations | |
| Chen, Gui-Qiang G.1,2,3 | |
| 2015-09-01 | |
| Source Publication | CHINESE ANNALS OF MATHEMATICS SERIES B
 |
| ISSN | 0252-9599 |
| Volume | 36Issue:5Pages:715-736 |
| Abstract | 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. |
| Keyword | Weak continuity Compensated compactness Nonlinear partial differential equations Euler equations Gauss-Codazzi-Ricci system |
| DOI | 10.1007/s11401-015-0973-x |
| Language | 英语 |
| Funding Project | UK EPSRC Science and Innovation Award[EP/E035027/1] ; UK EPSRC[EP/L015811/1] ; National Natural Science Foundation of China[10728101] ; Royal Society-Wolfson Research Merit Award (UK) |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000360569000005 |
| Publisher | SHANGHAI SCIENTIFIC TECHNOLOGY LITERATURE PUBLISHING HOUSE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/20716 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Chen, Gui-Qiang G. |
| Affiliation | 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 |
| Recommended Citation 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. |
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