Fluids, Elasticity, Geometry, and the Existence of Wrinkled Solutions
文献类型:期刊论文
作者 | Acharya, Amit1; Chen, Gui-Qiang G.2,3,4; Li, Siran2; Slemrod, Marshall5; Wang, Dehua6 |
刊名 | ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS |
出版日期 | 2017-12-01 |
卷号 | 226期号:3页码:1009-1060 |
ISSN号 | 0003-9527 |
DOI | 10.1007/s00205-017-1149-5 |
英文摘要 | 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. |
资助项目 | Rosi 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研究方向 | Mathematics ; Mechanics |
语种 | 英语 |
出版者 | SPRINGER |
WOS记录号 | WOS:000413000800003 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/26736] |
专题 | 中国科学院数学与系统科学研究院 |
作者单位 | 1.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 |
推荐引用方式 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. |
入库方式: OAI收割
来源:数学与系统科学研究院
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