Weak Continuity and Compactness for Nonlinear Partial Differential Equations

doi:10.1007/s11401-015-0973-x

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	Weak Continuity and Compactness for Nonlinear Partial Differential Equations
	Chen, Gui-Qiang G.1,2,3
	2015-09-01
发表期刊	CHINESE ANNALS OF MATHEMATICS SERIES B
ISSN	0252-9599
卷号	36 期号:5 页码:715-736
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.
关键词	Weak continuity Compensated compactness Nonlinear partial differential equations Euler equations Gauss-Codazzi-Ricci system
DOI	10.1007/s11401-015-0973-x
语种	英语
资助项目	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研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000360569000005
出版者	SHANGHAI SCIENTIFIC TECHNOLOGY LITERATURE PUBLISHING HOUSE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20716
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.