Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates

1998 ◽  
Vol 49 (6) ◽  
pp. 599-638 ◽  
Author(s):  
Pierre-Louis Lions ◽  
Benoît Perthame ◽  
Panagiotis E. Souganidis
Keyword(s):  
Gas Dynamics ◽  
Hyperbolic Systems ◽  
Entropy Solutions ◽  
Lagrangian Coordinates ◽  
Existence And Stability ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

scholarly journals Stability and convergence of the difference schemes for equations of isentropic gas dynamics in Lagrangian coordinates

2012 ◽  
Vol 91 (105) ◽  
pp. 137-153
Author(s):  
Piotr Matus ◽  
Dmitry Polyakov
Keyword(s):  
Gas Dynamics ◽  
A Priori Estimates ◽  
Initial Boundary ◽  
Stability And Convergence ◽  
Lagrangian Coordinates ◽  
Smooth Functions ◽  
Differential Problem ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas ◽  
The Difference

For the initial-boundary value problem (IBVP) if isentropic gas dynamics written in Lagrangian coordinates written in terms of Riemann invariants we show how to obtain necessary conditions for existence of global smooth solution using the Lax technique. Under these conditions we formulate the existence theorem in the class of piecewise-smooth functions. A priori estimates with respect to the input data for the difference scheme approximating this problem are obtained. The estimates of stability are proved using only restrictions on the initial and boundary conditions corresponding the differential problem. In the general case the estimates have been obtained only for the finite instant of time t < t0. The monotonicity has been proved in the both cases. The uniqueness and convergence of the difference solution are also considered. The results of the numerical experiment illustrating theoretical statements are given.

scholarly journals Soluciones globales para sistema isotérmico con fuente

2021 ◽  
Vol 39 (1) ◽  
Author(s):  
Xian Ting Wang
Keyword(s):  
Global Existence ◽  
Gas Dynamics ◽  
Short Note ◽  
Global Solutions ◽  
Momentum Equation ◽  
Global Existence Of Solutions ◽  
Existence And Stability ◽  
Isothermal System ◽  
Isentropic Gas Dynamics ◽  
Isentropic Gas

In this short note, we are concerned with the global existence of solutions to the isothermal system with source, where the inhomogeneous terms f(x,t,ρ,u)=b(x,t)ρ+(a′(x)/a(x))*ρu^2+α(x,t)ρu|u| are appeared in the momentum equation. Our work extended the results in the previous papers “Resonance for the Isothermal System of Isentropic Gas Dynamics” (Proc. A.M.S.139(2011),2821-2826), “Global Existence and Stability to the Polytropic Gas Dynamics with an Outer Force” (Appl. Math. Let-ters, 95(2019), 35-40) and “Existence of Global Solutions for Isentropic GasFlow with Friction” (Nonlinearity, 33(2020), 3940-3969), where the global solution was obtained for the source f(x,t,ρ,u)=(a′(x)/a(x))*ρu^2, f(x,t,ρ,u)=b(x,t)ρ, f(x,t,ρ,u)=α(x,t)ρu|u| respectively.

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.

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