| Issue |
Math. Model. Nat. Phenom.
Volume 16, 2021
|
|
|---|---|---|
| Article Number | 19 | |
| Number of page(s) | 22 | |
| DOI | https://doi.org/10.1051/mmnp/2021011 | |
| Published online | 23 March 2021 | |
Riemann problem with delta initial data for the two-dimensional steady pressureless isentropic relativistic Euler equations*
1
Department of Mathematics, Yunnan Normal University,
Kunming
650500, PR China.
2
College of Mathematics and Statistics, Xinyang Normal University,
Xinyang
464000, PR China.
** Corresponding author: yuzhang13120@126.com
Received:
13
September
2020
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.