TRANSONIC FLOWS AND ISOMETRIC EMBEDDINGS

被引：0
|
作者：
Chen, Gui-Qiang G. [1 ]
Slemrod, Marshall [1 ]
Wang, Dehua [1 ]
机构：
[1] Northwestern Univ, Dept Math, Evanston, IL 60208 USA
来源：
NONLINEAR CONSERVATION LAWS AND APPLICATIONS | 2011年 / 153卷
关键词：
Transonic flow; viscosity method; Euler equations; gas dynamics; compensated compactness; entropy solutions; isometric embedding; two-dimensional Riemannian manifold; Gauss-Codazzi system; negative Gauss curvature;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Transonic flows past an obstacle such as an airfoil are first considered. A viscous approximation to the steady transonic flow problem is presented, and its convergence is obtained by the method of compensated compactness. Then the isometric embedding problem in geometry is discussed. A fluid dynamic formulation of the Gauss-Codazzi system for the isometric embedding of two-dimensional Riemannian manifolds is provided, and an existence result of isometric immersions with negative Gauss curvature is given.
引用
收藏
页码：257 / 266
页数：10
相关论文
共 50 条
  • [31] Nontrivial Isometric Embeddings for Flat Spaces
    Paston, Sergey
    Zaitseva, Taisiia
    UNIVERSE, 2021, 7 (12)
  • [32] Isometric Hamming embeddings of weighted graphs
    Berleant, Joseph
    Sheridan, Kristin
    Condon, Anne
    Williams, Virginia Vassilevska
    Bathe, Mark
    DISCRETE APPLIED MATHEMATICS, 2023, 332 : 119 - 128
  • [33] Conformally isometric embeddings and Hawking temperature
    Dunajski, Maciej
    Tod, Paul
    CLASSICAL AND QUANTUM GRAVITY, 2019, 36 (12)
  • [34] IMPLICIT FUNCTION THEOREMS AND ISOMETRIC EMBEDDINGS
    JACOBOWITZ, H
    ANNALS OF MATHEMATICS, 1972, 95 (02) : 191 - +
  • [35] The spectrum and isometric embeddings of surfaces of revolution
    Engman, Martin
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2006, 49 (02): : 226 - 236
  • [36] THE GAUSS EQUATIONS AND RIGIDITY OF ISOMETRIC EMBEDDINGS
    BERGER, E
    BRYANT, R
    GRIFFITHS, P
    DUKE MATHEMATICAL JOURNAL, 1983, 50 (03) : 803 - 892
  • [37] ISOMETRIC EMBEDDINGS INTO CUBE-HYPERGRAPHS
    BUROSCH, G
    CECCHERINI, PV
    DISCRETE MATHEMATICS, 1995, 137 (1-3) : 77 - 85
  • [38] Isometric embeddings of the surfaces of the Platonic solids
    Shtogrin, M. I.
    RUSSIAN MATHEMATICAL SURVEYS, 2007, 62 (02) : 395 - 397
  • [39] Isometric embeddings of Polish ultrametric spaces
    Malicki, Maciej
    TOPOLOGY AND ITS APPLICATIONS, 2012, 159 (16) : 3426 - 3431
  • [40] ISOMETRIC EMBEDDINGS VIA HEAT KERNEL
    Wang, Xiaowei
    Zhu, Ke
    JOURNAL OF DIFFERENTIAL GEOMETRY, 2015, 99 (03) : 497 - 538
12345