Global existence and asymptotic behavior for the full compressible Euler equations with damping in $\mathbb R^3$

2017 ◽  
Vol 119 (2) ◽  
pp. 147-163
Author(s):  
Guochun Wu ◽  
Zhensheng Gao
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Euler Equations ◽  
Compressible Euler Equations ◽  
Compressible Euler

scholarly journals Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Huimin Yu
Keyword(s):  
Asymptotic Behavior ◽  
Euler Equations ◽  
Boundary Effect ◽  
Nonlinear Damping ◽  
Compressible Euler Equations ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Slip Boundary ◽  
Compressible Euler ◽  
Linear Damping

The asymptotic behavior (as well as the global existence) of classical solutions to the 3D compressible Euler equations are considered. For polytropic perfect gas(P(ρ)=P0ργ), time asymptotically, it has been proved by Pan and Zhao (2009) that linear damping and slip boundary effect make the density satisfying the porous medium equation and the momentum obeying the classical Darcy's law. In this paper, we use a more general method and extend this result to the 3D compressible Euler equations with nonlinear damping and a more general pressure term. Comparing with linear damping, nonlinear damping can be ignored under small initial data.

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