The Exact Solution to the 3D Vortex Compressible Euler Equation and the Clay Millennium Problem Generalization

2019 ◽  
pp. 71-81
Author(s):  
S. G. Chefranov ◽  
A. S. Chefranov
Keyword(s):  
Exact Solution ◽  
Euler Equation ◽  
Compressible Euler Equation ◽  
Compressible Euler

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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