scholarly journals Optimal time-dependent lower bound on density for classical solutions of 1-D compressible Euler equations

2017 ◽  
Vol 66 (3) ◽  
pp. 725-740 ◽  
Author(s):  
Geng Chen
Keyword(s):  
Lower Bound ◽  
Euler Equations ◽  
Time Dependent ◽  
Compressible Euler Equations ◽  
Classical Solutions ◽  
Optimal Time ◽  
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.

scholarly journals The blowup of solutions for 3-D axisymmetric compressible Euler equations

1999 ◽  
Vol 154 ◽  
pp. 157-169 ◽  
Author(s):  
Huicheng Yin ◽  
Qingjiu Qiu
Keyword(s):  
Asymptotic Expansion ◽  
Initial Data ◽  
Euler Equations ◽  
Blow Up ◽  
Three Dimensional ◽  
Compressible Euler Equations ◽  
Classical Solutions ◽  
Complete Asymptotic Expansion ◽  
Blowup Of Solutions ◽  
Compressible Euler

AbstractIn this paper, for three dimensional compressible Euler equations with small perturbed initial data which are axisymmetric, we prove that the classical solutions have to blow up in finite time and give a complete asymptotic expansion of lifespan.

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