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Fluids, Elasticity, Geometry, and the Existence of Wrinkled Solutions
Acharya, Amit1; Chen, Gui-Qiang G.2,3,4; Li, Siran2; Slemrod, Marshall5; Wang, Dehua6
2017-12-01
Source PublicationARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
ISSN0003-9527
Volume226Issue:3Pages:1009-1060
Abstract

We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we develop such connections for the case of two spatial dimensions, and demonstrate that the continuum mechanical equations can be mapped into a corresponding geometric framework and the inherent direct application of the theory of isometric embeddings and the Gauss-Codazzi equations through examples for the Euler equations for fluids and the Euler-Lagrange equations for elastic solids. These results show that the geometric theory provides an avenue for addressing the admissibility criteria for nonlinear conservation laws in continuum mechanics.

DOI10.1007/s00205-017-1149-5
Language英语
Funding ProjectRosi and Max Varon Visiting Professorship at the Weizmann Institute of Science, Rehovot, Israel ; ARO[W911NF-15-1-0239] ; UK Engineering and Physical Sciences Research Council[EP/E035027/1] ; UK Engineering and Physical Sciences Research Council[EP/L015811/1] ; Royal Society-Wolfson Research Merit Award (UK) ; UK EPSRC Science and Innovation award[EP/E035027/1] ; Simons Collaborative Research Grant[232531] ; NSF[DMS-1312800] ; NSF[DMS-1613213] ; [NSF-CMMI-1435624] ; [NSF-DMS-1434734]
WOS Research AreaMathematics ; Mechanics
WOS SubjectMathematics, Applied ; Mechanics
WOS IDWOS:000413000800003
PublisherSPRINGER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26737
Collection中国科学院数学与系统科学研究院
Affiliation1.Carnegie Mellon Univ, Civil & Environm Engn, Pittsburgh, PA 15213 USA
2.Univ Oxford, Math Inst, Oxford OX2 6GG, England
3.Chinese Acad Sci, AMSS, Beijing 100190, Peoples R China
4.Chinese Acad Sci, UCAS, Beijing 100190, Peoples R China
5.Univ Wisconsin, Dept Math, Madison, WI 53706 USA
6.Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
Recommended Citation
GB/T 7714
Acharya, Amit,Chen, Gui-Qiang G.,Li, Siran,et al. Fluids, Elasticity, Geometry, and the Existence of Wrinkled Solutions[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,2017,226(3):1009-1060.
APA Acharya, Amit,Chen, Gui-Qiang G.,Li, Siran,Slemrod, Marshall,&Wang, Dehua.(2017).Fluids, Elasticity, Geometry, and the Existence of Wrinkled Solutions.ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS,226(3),1009-1060.
MLA Acharya, Amit,et al."Fluids, Elasticity, Geometry, and the Existence of Wrinkled Solutions".ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS 226.3(2017):1009-1060.
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