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

Huahui  Li; Zhiqiang  Shao

doi:10.3934/cpaa.2016041

Article Contents

2016, Volume 15, Issue 6: 2373-2400. Doi: 10.3934/cpaa.2016041

This issue Previous Article Elliptic operators with unbounded diffusion coefficients perturbed by inverse square potentials in $L^p$--spaces Next Article Evolutionary, symmetric $p$-Laplacian. Interior regularity of time derivatives and its consequences

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

Huahui Li^1, and
Zhiqiang Shao^1,

1.
College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116

Received: February 29, 2016

Revised: June 30, 2016

Published: October 2016

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Abstract

The Riemann solutions for the relativistic Euler equations for generalized Chaplygin gas are considered. It is rigorously proved that, as the pressure vanishes, they tend to the two kinds of Riemann solutions to the zero-pressure relativistic Euler equations, which include a delta shock formed by a weighted $\delta$-measure and a vacuum state.

Keywords:

Relativistic Euler equations,
generalized Chaplygin gas,
zero-pressure relativistic Euler equations,
delta shock wave,
vacuum state,
vanishing pressure limits.

Mathematics Subject Classification: 35L65, 35L67.

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