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Stability and Unstability of the Standing Wave to Euler Equations

Part of: Hyperbolic equations and systems Equations of mathematical physics and other areas of application Partial differential equations Representations of solutions

Published online by Cambridge University Press:  18 January 2017

Xiuli Tang ,
Xiuqing Wang  and
Ganshan Yang
Xiuli Tang
Affiliation:
College of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350117, China
Xiuqing Wang
Affiliation:
College of Mathematics and Computer Science, Yunnan Nationalities University, Kunming, Yunnan 650504, China
Ganshan Yang*
Affiliation:
College of Mathematics and Computer Science, Yunnan Nationalities University, Kunming, Yunnan 650504, China
*
*Corresponding author. Email:yangganshan@aliyun.com (G. S. Yang)
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Abstract

In this paper, we first discuss the well-posedness of linearizing equations, and then study the stability and unstability of the 3-D compressible Euler Equation, by analysing the existence of saddle point. In addition, we give the existence of local solutions of the compressible Euler equation.

Keywords

Euler EquationsLie Groupwell-posednesssaddle point

MSC classification

Secondary: 35Q31: Euler equations 35L04: Initial-boundary value problems for first-order hyperbolic equations 35C07: Traveling wave solutions 35B35: Stability
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 4 , August 2017 , pp. 818 - 838
Copyright
Copyright © Global-Science Press 2017 

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