scholarly journals Vanishing Viscosity Approach to the Compressible Euler Equations for Transonic Nozzle and Spherically Symmetric Flows

2018 ◽  
Vol 229 (3) ◽  
pp. 1239-1279 ◽  
Author(s):  
Gui-Qiang G. Chen ◽  
Matthew R. I. Schrecker
Keyword(s):  
Euler Equations ◽  
Compressible Euler Equations ◽  
Spherically Symmetric ◽  
Vanishing Viscosity ◽  
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.

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