Exact solutions to Euler equation and Navier-Stokes equation

被引：21
作者：
Liu, Mingshuo [1 ]
Li, Xinyue [1 ]
Zhao, Qiulan [1 ]
机构：
[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2019年 / 70卷 / 02期
关键词：
Euler equation; Navier-Stokes equation; Lie symmetry analysis method; Backlund transformation; TRAVELING-WAVE SOLUTIONS; ROSSBY SOLITARY WAVES; LIE SYMMETRY ANALYSIS; LUMP-KINK SOLUTIONS; BACKLUND-TRANSFORMATIONS; EXPLICIT SOLUTIONS; WELL-POSEDNESS; WEAK SOLUTIONS; EXISTENCE;
D O I：
10.1007/s00033-019-1088-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Lie symmetry analysis method and Backlund transformation method are proposed for finding similarity reduction and exact solutions to Euler equation and Navier-Stokes equation, respectively. By using symmetry reduction method, we reduce nonlinear partial differential equation to nonlinear ordinary differential equation. The infinitesimal generators and the soliton solutions to the Euler equation are obtained by Lie symmetry analysis method. Furthermore, the Backlund transformation of the Navier-Stokes equation is proposed to obtain the exact solution. We obtain the exact solutions to Navier-Stokes equation on background flow.
引用
收藏
页数：13
相关论文
共 48 条
  • [1] ABLOWITZ MJ, 2000, SOLITONS NONLINEAR E
  • [2] [Anonymous], 1986, Theoretical Physics. Hydrodynamics
  • [3] On the existence of global weak solutions to the Navier-Stokes equations for viscous compressible and heat conducting fluids
    Bresch, Didier
    Desjardins, Benoit
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 87 (01): : 57 - 90
  • [4] Nonlocal symmetry, Darboux transformation and soliton-cnoidal wave interaction solution for the shallow water wave equation
    Chen, Junchao
    Ma, Zhengyi
    Hu, Yahong
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 460 (02) : 987 - 1003
  • [5] Chen Y, 2008, PHYS REV D, V78, P909
  • [6] CRE Solvability, Nonlocal Symmetry and Exact Interaction Solutions of the Fifth-Order Modified Korteweg-de Vries Equation
    Cheng, Wen-Guang
    Qiu, De-Qin
    Yu, Bo
    [J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 2017, 67 (06) : 637 - 642
  • [7] WELL-POSEDNESS OF THE FREE-BOUNDARY COMPRESSIBLE 3-D EULER EQUATIONS WITH SURFACE TENSION AND THE ZERO SURFACE TENSION LIMIT
    Coutand, Daniel
    Hole, Jason
    Shkoller, Steve
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2013, 45 (06) : 3690 - 3767
  • [8] Dong HH, 2016, J NONLINEAR SCI APPL, V9, P5107
  • [9] N-SOLITON-LIKE SOLUTIONS AND BACKLUND TRANSFORMATIONS FOR A NON-ISOSPECTRAL AND VARIABLE-COEFFICIENT MODIFIED KORTEWEG-DE VRIES EQUATION
    Feng, Qian
    Gao, Yi-Tian
    Meng, Xiang-Hua
    Yu, Xin
    Sun, Zhi-Yuan
    Xu, Tao
    Tian, Bo
    [J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2011, 25 (05): : 723 - 733
  • [10] Time-Space Fractional Coupled Generalized Zakharov-Kuznetsov Equations Set for Rossby Solitary Waves in Two-Layer Fluids
    Fu, Lei
    Chen, Yaodeng
    Yang, Hongwei
    [J]. MATHEMATICS, 2019, 7 (01)
12345