The global Hölder-continuous solution of isentropic gas dynamics

1993 ◽  
Vol 123 (2) ◽  
pp. 231-238 ◽  
Author(s):  
Yun-Guang Lu
Keyword(s):  
Cauchy Problem ◽  
Gas Dynamics ◽  
Continuous Solution ◽  
Hölder Continuous ◽  
Vanishing Viscosity ◽  
Equations Of Gas Dynamics ◽  
The Cauchy Problem ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

SynopsisThis paper considers the Cauchy problem for the isentropic equations of gas dynamics in Euler coordinates ρt + (ρu)x = 0, (ρu)t + (ρu)2 + P(ρ))x=0 and gives the Hölder-continuous solution by applying the method of vanishing viscosity.

Vanishing viscosity for non-isentropic gas dynamics with interacting shocks

2016 ◽  
Vol 36 (6) ◽  
pp. 1699-1720 ◽  
Author(s):  
Xiaoding SHI ◽  
Yan YONG ◽  
Yinglong ZHANG
Keyword(s):  
Gas Dynamics ◽  
Vanishing Viscosity ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

LARGE TIME DECAY OF SOLUTIONS TO ISENTROPIC GAS DYNAMICS WITH SPHERICAL SYMMETRY

2009 ◽  
Vol 06 (02) ◽  
pp. 371-387
Author(s):  
NAOKI TSUGE
Keyword(s):  
Spherical Symmetry ◽  
Gas Dynamics ◽  
Large Time ◽  
Approximate Solutions ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Time Decay ◽  
Decay Of Solutions ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

We consider the large time behavior of solutions to isentropic gas dynamics with spherical symmetry. In the present paper, we show the decay of the pressure in particular. To do this, we investigate approximate solutions constructed by a difference scheme.

scholarly journals Double asymptotic expansion of the resolving operator of the cauchy problem for the line-arized system of gas dynamics

2019 ◽  
Vol 484 (2) ◽  
pp. 134-137
Author(s):  
A. I. Allilueva ◽  
A. I. Shafarevich
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Expansion ◽  
Gas Dynamics ◽  
Acoustic Modes ◽  
Small Viscosity ◽  
The Cauchy Problem ◽  
Linearized System

We obtain double asymptotic expansion (with respect to smoothness and small viscosity) of the resolving operator of the Cauchy problem for the linearized system of gas dynamics. We derive estimates for the summands and for the residual in the Sobolev scale.We describe explicitly hydrodynamic and acoustic modes.

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