Stability of Riemann solution for the relativistic Euler equations with Chaplygin gas under the perturbation of initial data

The structural stability of the Riemann solution for the relativistic Euler equations (REE) with Chaplygin gas is investigated. First, we perturb the Riemann initial data by introducing three piecewise constant states and rigorously establish the global structures of solutions to the perturbed Riemann problem. Then, by imposing the perturbed parameter ε tends to zero, we show that there is no mass concentration even if the initial perturbed density depends on ε. This result implies that the Riemann solutions for the REE with Chaplygin gas are stable under the local small perturbation of the initial data.