Global solution of an initial-value problem for two-dimensional compressible Euler equations
type: Item
instance of: scholarly article
title: Global solution of an initial-value problem for two-dimensional compressible Euler equations
zbMATH Open document ID: 1007.35077
author: Jiequan Li
published in: Journal of Differential Equations
publication date: 2003-03-20T00:00:00Z
review text: The author proves the existence of the unique global continuous solution for compressible Euler equations which describe an expansion of a gas wedge into vacuum. First, by hodograph transformation the governing quasi-stationary partial differential equations are reduced to a system of two inhomogeneous linearly degenerate equations in phase space under the condition that the flow is irrotational. Then the title problem is shown to be a uniformly hyperbolic Goursat-type problem for these two equations in the supersonic domain. A standard application of Gronwall's inequality implies the existence of the solution.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 1744188
zbMATH Keywords: initial value problem
zbMATH Keywords: uniqueness
zbMATH Keywords: expansion of wedge into vacuum
zbMATH Keywords: existence
zbMATH Keywords: global continuous solution
zbMATH Keywords: compressible Euler equations
zbMATH Keywords: hodograph transformation
zbMATH Keywords: phase space
zbMATH Keywords: uniformly hyperbolic Goursat-type problem
zbMATH Keywords: supersonic domain
zbMATH Keywords: Gronwall's inequality
MaRDI profile type: Publication
OpenAlex ID: W2040895685
cites work: On the 2-D Riemann problem for the compressible Euler equations I: Interaction of shocks and rarefaction waves
cites work: Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics
cites work: Global BV solutions of compressible Euler equations with spherical symmetry and damping
cites work: Q5559035
cites work: Q4852353
cites work: Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes
cites work: Q3762928
cites work: Q4265266
cites work: Q5559036
cites work: Q5566685
cites work: Classification of the Riemann Problem for Two-Dimensional Gas Dynamics
cites work: Q4314474
cites work: Numerical Solution of the Riemann Problem for Two-Dimensional Gas Dynamics
cites work: Systems of conservation laws. Two-dimensional Riemann problems
cites work: Conjecture on the Structure of Solutions of the Riemann Problem for Two-Dimensional Gas Dynamics Systems
cites work: Axisymmetric solutions of the Euler equations for polytropic gases
DOI: 10.1006/JDEQ.2001.4025
description: scientific article; zbMATH DE number 1744188