The Incompressible Limit and the Initial Layer of the Compressible Euler Equation in ℝn+

1997 ◽  
Vol 20 (11) ◽  
pp. 945-958 ◽  
Author(s):  
Tatsuo Iguchi
Keyword(s):  
Euler Equation ◽  
Incompressible Limit ◽  
Compressible Euler Equation ◽  
Initial Layer ◽  
Compressible Euler

Initial layer and incompressible limit for Euler–Poisson equation in nonthermal plasma

2019 ◽  
Vol 29 (09) ◽  
pp. 1733-1751
Author(s):  
Tao Luo ◽  
Shu Wang ◽  
Yan-Lin Wang
Keyword(s):  
Asymptotic Expansion ◽  
Poisson Equation ◽  
Nonthermal Plasma ◽  
Approximate Solutions ◽  
Singular Limit ◽  
Incompressible Limit ◽  
Incompressible Euler Equation ◽  
Initial Layer ◽  
Compressible Euler ◽  
Incompressible Euler

The singular limit from compressible Euler–Poisson equation in nonthermal plasma to incompressible Euler equation with an ill-prepared initial data is investigated in this paper by constructing approximate solutions of the appropriate order via an asymptotic expansion. Nonlinear asymptotic stability of initial layer approximation is established with the convergence rate.

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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