The limits of Riemann solutions for the isentropic Euler system with extended Chaplygin gas

ABSTRACT

The Riemann problem for the isentropic Euler system with the state equation for the extended Chaplygin gas is considered, and the Riemann solutions are constructed completely for all the cases. The limiting relations of Riemann solutions for the isentropic Euler system with the state equation from the extended Chaplygin gas to the Chaplygin gas are derived in detail when the corrected term tends to zero. The formation of delta shock wave solution and two-contact-discontinuity solution is investigated during the process of taking the limit.

KEYWORDS:

• Extended Chaplygin gas
• Chaplygin gas
• delta shock wave
• Riemann problem
• isentropic Euler system

AMS SUBJECT CLASSIFICATIONS:

• 35L65
• 35L67
• 76N15

Acknowledgements

The authors are very grateful to the anonymous referee for the corrections and suggestions which improve the original manuscript greatly.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by Natural Science Foundation of China [grant number 11441002]; Shandong Provincial Natural Science Foundation [grant number ZR2014AM024].