Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for generalized Chaplygin gas

DOI10.3934/cpaa.2016041zbMath1354.35080OpenAlexW2530927068MaRDI QIDQ334518

Huahui Li, Zhi-Qiang Shao

Publication date: 1 November 2016

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2016041

zbMATH Keywords

vacuum statedelta shock wavegeneralized Chaplygin gasrelativistic Euler equationsvanishing pressure limitszero-pressure relativistic Euler equations

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Shock waves and blast waves in fluid mechanics (76L05) Hyperbolic conservation laws (35L65) Euler equations (35Q31)

Related Items (21)

The Riemann problem for the relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation ⋮ Instability solutions for the Rayleigh-Taylor problem of non-homogeneous viscoelastic fluids in bounded domains ⋮ Concentration and Cavitation in the Vanishing Pressure Limit of Solutions to a 3 × 3 Generalized Chaplygin Gas Equations ⋮ Delta shock formation for the isothermal and logarithmic-corrected Chaplygin Euler equations ⋮ Exact Riemann solver for non-convex relativistic hydrodynamics ⋮ Concentration in vanishing adiabatic exponent limit of solutions to the Aw–Rascle traffic model ⋮ The cavitation and concentration of Riemann solutions for the isentropic Euler equations with isothermal dusty gas ⋮ Concentration and cavitation in the vanishing pressure limit of solutions to the relativistic Euler equations with the logarithmic equation of state ⋮ Comparison of Riemann solutions for non-isentropic modified and pure Chaplygin gas dynamics ⋮ The transition of Riemann solutions of the modified Chaplygin gas equations with friction to the solutions of the Chaplygin gas equations ⋮ The singular limits of solutions to the Riemann problem for the liquid–gas two-phase isentropic flow model ⋮ Delta shocks and vacuums to the isentropic Euler equations with the flux perturbation for van der Waals gas ⋮ Solutions with concentration and cavitation to the Riemann problem for the isentropic relativistic Euler system for the extended Chaplygin gas ⋮ The limits of Riemann solutions for the isentropic Euler system with extended Chaplygin gas ⋮ The vanishing adiabatic exponent limits of Riemann solutions to the isentropic Euler equations for power law with a Coulomb-like friction term ⋮ Concentration and cavitation phenomena of Riemann solutions for the isentropic Euler system with the logarithmic equation of state ⋮ The limiting behavior of the Riemann solutions of non-isentropic modified Chaplygin gas dynamics ⋮ Concentration in the zero-exponent limit of solutions to the isentropic Euler equations for extended Chaplygin gas ⋮ Vanishing magnetic field limits of solutions to the isentropic Chaplygin gas magnetogasdynamics equations ⋮ On effect of surface tension in the Rayleigh-Taylor problem of stratified viscoelastic fluids ⋮ Formation of vacuum state and delta shock wave for the relativistic Euler system for polytropic gas with the varying \(\gamma\)-law

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