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Limits of solutions to the relativistic Euler equations for modified Chaplygin gas by flux approximation. (English) Zbl 1459.35316

Summary: We study the Riemann problem and flux-approximation limits of solutions to the relativistic Euler equations with the state equation for modified Chaplygin gas. The limits of Riemann solutions for the relativistic modified Chaplygin gas equations and the corresponding flux-approximation system are discussed when the pressure term and flux-perturbation parameters tend to zero. It is rigorously proved that, as the pressure and flux approximations vanish respectively, any two-shock-wave Riemann solution tends to a delta-shock solution to the pressureless relativistic Euler equations, and the intermediate density between them tends to a weighted \(\delta\)-measure that forms a delta shock wave. Correspondingly, any two-rarefaction-wave solution becomes two contact discontinuities connecting the constant states and vacuum states, which form a vacuum solution.

MSC:

35Q31 Euler equations
35L65 Hyperbolic conservation laws
35L67 Shocks and singularities for hyperbolic equations
35Q75 PDEs in connection with relativity and gravitational theory
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