Math. Model. Nat. Phenom.
Volume 16, 2021
|Number of page(s)||22|
|Published online||23 March 2021|
Riemann problem with delta initial data for the two-dimensional steady pressureless isentropic relativistic Euler equations*
Department of Mathematics, Yunnan Normal University,
650500, PR China.
2 College of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, PR China.
** Corresponding author: email@example.com
Accepted: 31 January 2021
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.
Mathematics Subject Classification: 35L65 / 35L67 / 76N10
Key words: Relativistic Euler equations / steady flow / Riemann problem / delta shock wave / delta contact discontinuity
Supported by National Natural Science Foundation of China (11501488), Yunnan Applied Basic Research Projects (2018FD015), the Scientific Research Foundation Project of Yunnan Education Department (2018JS150), the PhD Research Startup Foundation of Yunnan Normal University (2016zb012), Nan Hu Young Scholar Supporting Program of XYNU.
© The authors. Published by EDP Sciences, 2021
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