Abstract
This paper studies a Riemann problem for the isentropic Euler equations and addresses two gaps in the literature concerning positive pressures. Such study is made using a product of distributions and a solution concept that extends the classical solution concept. Under certain conditions, even for positive pressures, it is shown that the Riemann problem has solutions, which are \(\delta \)-shock waves. As particular cases, this work examines polytropic gases, pressureless gases, and Chaplygin gases.
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Acknowledgements
Supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2019. I cordially thank the referees for the helpful comments and valuable suggestions which significantly improved this paper.
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Paiva, A. Formation of \(\delta \)-shock waves in isentropic fluids. Z. Angew. Math. Phys. 71, 110 (2020). https://doi.org/10.1007/s00033-020-01332-6
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DOI: https://doi.org/10.1007/s00033-020-01332-6
Keywords
- Isentropic Euler equations
- Conservation laws
- Nonlinear PDEs
- Products of distributions
- Shock-waves
- Delta-shock waves