Riemann problem with delta initial data for the two-dimensional steady pressureless isentropic relativistic Euler equations

Yu Zhang¹ ; Yanyan Zhang²

¹ Department of Mathematics, Yunnan Normal University, Kunming 650500, PR China.
² College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, PR China.

Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 19.

Résumé

The Riemann problem for the two-dimensional steady pressureless isentropic relativistic Euler equations with delta initial data is studied. First, the perturbed Riemann problem with three pieces constant initial data is solved. Then, via discussing the limits of solutions to the perturbed Riemann problem, the global solutions of Riemann problem with delta initial data are completely constructed under the stability theory of weak solutions. Interestingly, the delta contact discontinuity is found in the Riemann solutions of the two-dimensional steady pressureless isentropic relativistic Euler equations with delta initial data.

Détail

DOI : 10.1051/mmnp/2021011

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