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

页数：13

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