Global Existence and Stability of Shock Front Solution to 1-D Piston Problem for Exothermically Reacting Euler Equations

2020 ◽  
Vol 22 (2) ◽  
Author(s):  
Jie Kuang ◽  
Qin Zhao
Keyword(s):  
Global Existence ◽  
Shock Front ◽  
Euler Equations ◽  
Piston Problem ◽  
Front Solution ◽  
Existence And Stability ◽  
Shock Front Solution

GLOBAL EXISTENCE OF SHOCK FRONT SOLUTIONS TO THE AXIALLY SYMMETRIC PISTON PROBLEM FOR COMPRESSIBLE FLUIDS

2004 ◽  
Vol 01 (01) ◽  
pp. 51-84 ◽  
Author(s):  
SHUXING CHEN ◽  
ZEJUN WANG ◽  
YONGQIAN ZHANG
Keyword(s):  
Global Existence ◽  
Shock Front ◽  
Compressible Fluids ◽  
Axially Symmetric ◽  
Piston Problem ◽  
Front Solution ◽  
Glimm Scheme ◽  
Front Solutions ◽  
Shock Front Solution

In this paper, we study the axially symmetric piston problem for compressible fluids when the velocity of the piston is a perturbation of a constant. Under the assumptions that both the velocity of the piston and the density of the gas outside the piston are small, we prove the global existence of a shock front solution by using a modified Glimm scheme.

Asymptotic decay to relaxation shock fronts in two dimensions

2001 ◽  
Vol 131 (6) ◽  
pp. 1385-1410 ◽  
Author(s):  
Hailiang Liu
Keyword(s):  
Shock Front ◽  
Initial Perturbation ◽  
Two Dimensions ◽  
Decay Rates ◽  
Front Solution ◽  
Asymptotic Decay ◽  
Planar Shock ◽  
Spatial Dimensions ◽  
Shock Front Solution ◽  
Shock Fronts

We prove nonlinear stability of planar shock fronts for certain relaxation systems in two spatial dimensions. If the subcharacteristic condition is assumed and the initial perturbation is sufficiently small and the mass carried by the perturbations is not necessarily finite, then the solution converges to a shifted planar shock front solution as time t ↑ ∞. The asymptotic phase shift of shock fronts is, in general, non-zero and governed by a similarity solution to the heat equation. The asymptotic decay rate to the shock front is proved to be t−1/4 in L∞(R2) without imposing extra decay rates in space for the initial perturbations. The proofs are based on an elementary weighted energy analysis to the error equation.

Global Existence for the Two-Dimensional Euler Equations in a Critical Besov Space

2011 ◽  
Vol 271-273 ◽  
pp. 791-796
Author(s):  
Kun Qu ◽  
Yue Zhang
Keyword(s):  
Global Existence ◽  
Transport Equation ◽  
Besov Space ◽  
Euler Equations ◽  
Existence Result ◽  
Two Dimensional ◽  
Critical Besov Space ◽  
Global Existence Result

In this paper we prove the global existence for the two-dimensional Euler equations in the critical Besov space. Making use of a new estimate of transport equation and Littlewood-Paley theory, we get the global existence result.

Sign in / Sign up

Export Citation Format

Share Document