scholarly journals Large time behavior of solutions for compressible Euler equations with damping in R3

2012 ◽  
Vol 252 (2) ◽  
pp. 1546-1561 ◽  
Author(s):  
Zhong Tan ◽  
Guochun Wu
Keyword(s):  
Euler Equations ◽  
Large Time ◽  
Large Time Behavior ◽  
Compressible Euler Equations ◽  
Time Behavior ◽  
Compressible Euler

Remarks on spherically symmetric solutions of the compressible Euler equations

1997 ◽  
Vol 127 (2) ◽  
pp. 243-259 ◽  
Author(s):  
Gui-Qiang Chen
Keyword(s):  
Euler Equations ◽  
Large Time ◽  
Blow Up ◽  
Cauchy Data ◽  
Blast Waves ◽  
Compressible Euler Equations ◽  
Spherically Symmetric ◽  
Asymptotic Decay ◽  
Compressible Euler ◽  
Spherically Symmetric Solutions

Some evidence indicates that spherically symmetric solutions of the compressible Euler equations blow up near the origin at some time under certain circumstances (cf. [4,19]). In this paper, we observe a criterion for L∞ Cauchy data of arbitrarily large amplitude to ensure the existence of L∞ spherically symmetric solutions in the large, which model outgoing blast waves and large-time asymptotic solutions. The equilibrium states of the solutions and their asymptotic decay to such states are analysed. Some remarks on global spherically symmetric solutions are discussed.

scholarly journals The global Cauchy problem for compressible Euler equations with a nonlocal dissipation

2019 ◽  
Vol 29 (01) ◽  
pp. 185-207 ◽  
Author(s):  
Young-Pil Choi
Keyword(s):  
Global Existence ◽  
Euler Equations ◽  
Large Time ◽  
Strong Solutions ◽  
Large Time Behavior ◽  
Local Alignment ◽  
Time Behavior ◽  
Unique Strong Solution ◽  
Global Existence And Uniqueness ◽  
Isothermal Euler Equations

This paper studies the global existence and uniqueness of strong solutions and its large-time behavior for the compressible isothermal Euler equations with a nonlocal dissipation. The system is rigorously derived from the kinetic Cucker–Smale flocking equation with strong local alignment forces and diffusions through the hydrodynamic limit based on the relative entropy argument. In a perturbation framework, we establish the global existence of a unique strong solution for the system under suitable smallness and regularity assumptions on the initial data. We also provide the large-time behavior of solutions showing the fluid density and the velocity converge to its averages exponentially fast as time goes to infinity.

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