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Weak Continuity and Compactness for Nonlinear Partial Differential Equations
Chen, Gui-Qiang G.1,2,3
2015-09-01
Source PublicationCHINESE ANNALS OF MATHEMATICS SERIES B
ISSN0252-9599
Volume36Issue:5Pages:715-736
AbstractThis 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.
KeywordWeak continuity Compensated compactness Nonlinear partial differential equations Euler equations Gauss-Codazzi-Ricci system
DOI10.1007/s11401-015-0973-x
Language英语
Funding ProjectUK 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 AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000360569000005
PublisherSHANGHAI SCIENTIFIC TECHNOLOGY LITERATURE PUBLISHING HOUSE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/20716
Collection中国科学院数学与系统科学研究院
Affiliation1.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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