scholarly journals Smooth solutions of the one-dimensional compressible Euler equation with gravity

2016 ◽  
Vol 260 (1) ◽  
pp. 708-732 ◽  
Author(s):  
Cheng-Hsiung Hsu ◽  
Song-Sun Lin ◽  
Chi-Ru Yang
Keyword(s):  
Euler Equation ◽  
Compressible Euler Equation ◽  
Smooth Solutions ◽  
One Dimensional ◽  
Compressible Euler ◽  
The One

Stability and Unstability of the Standing Wave to Euler Equations

2017 ◽  
Vol 9 (4) ◽  
pp. 818-838
Author(s):  
Xiuli Tang ◽  
Xiuqing Wang ◽  
Ganshan Yang
Keyword(s):  
Saddle Point ◽  
Euler Equation ◽  
Euler Equations ◽  
Standing Wave ◽  
Well Posedness ◽  
Compressible Euler Equation ◽  
Compressible Euler ◽  
Local Solutions ◽  
The Stability

AbstractIn 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.

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