Global solution of an initial-value problem for two-dimensional compressible Euler equations

DOI10.1006/jdeq.2001.4025zbMath1007.35077OpenAlexW2040895685MaRDI QIDQ1598375

Jiequan Li

Publication date: 20 March 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/8a931520372c645ec0d2493c064f8c90b016b5da

zbMATH Keywords

existencehodograph transformationuniquenessinitial value problemphase spacecompressible Euler equationsGronwall's inequalityexpansion of wedge into vacuumglobal continuous solutionsupersonic domainuniformly hyperbolic Goursat-type problem

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

Related Items

Expansion of a wedge of non-ideal gas into vacuum ⋮ On two-dimensional gas expansion for pressure-gradient equations of Euler system ⋮ The expansion of a wedge of gas into vacuum with small angle in two-dimensional isothermal flow ⋮ Interaction of rarefaction waves of the two-dimensional self-similar Euler equations ⋮ The Pressure-Gradient System on Non-smooth Domains ⋮ Simple waves for two-dimensional compressible pseudo-steady Euler system ⋮ Degenerate Goursat-type boundary value problems arising from the study of two-dimensional isothermal Euler equations ⋮ The two-dimensional Riemann problem for Chaplygin gas dynamics with three constant states ⋮ Two dimensional relativistic Euler equations in a convex duct ⋮ The Analytical Solutions for theN-Dimensional Damped Compressible Euler Equations ⋮ The interaction of rarefaction waves of a two-dimensional nonlinear wave system ⋮ Semi-hyperbolic patches of solutions to the two-dimensional nonlinear wave system for Chaplygin gases ⋮ The two dimensional gas expansion problem of the Euler equations for the generalized Chaplygin gas ⋮ Explicitly self-similar solutions for the Euler/Navier-Stokes-Korteweg equations in \(R^N\) ⋮ Semi-hyperbolic patches of solutions to the two-dimensional Euler equations ⋮ Two-dimensional Riemann problems for the compressible Euler system

Cites Work

• Axisymmetric solutions of the Euler equations for polytropic gases
• Global BV solutions of compressible Euler equations with spherical symmetry and damping
• On the 2-D Riemann problem for the compressible Euler equations I: Interaction of shocks and rarefaction waves
• Systems of conservation laws. Two-dimensional Riemann problems
• Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics
• Conjecture on the Structure of Solutions of the Riemann Problem for Two-Dimensional Gas Dynamics Systems
• Classification of the Riemann Problem for Two-Dimensional Gas Dynamics
• Numerical Solution of the Riemann Problem for Two-Dimensional Gas Dynamics
• Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes
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