Abstract
We are concerned with the vanishing flux-approximation limits of solutions to the isentropic relativistic Euler equations governing isothermal perfect fluid flows. The Riemann problem with a two-parameter flux approximation including pressure term is first solved. Then, we study the limits of solutions when the pressure and two-parameter flux approximation vanish, respectively. It is shown that, any two-shock-wave Riemann solution converges to a delta-shock solution of the pressureless relativistic Euler equations, and the intermediate density between these two shocks tends to a weighted δ-measure that forms a delta shock wave. By contract, any two-rarefaction-wave solution tends to a two-contact-discontinuity solution of the pressureless relativistic Euler equations, and the intermediate state in between tends to a vacuum state.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11501488
Funding source: Nan Hu Young Scholar Supporting Program of XYNU
Funding source: Scientific Research Foundation Project of Yunnan Education Department
Award Identifier / Grant number: 2018JS150
Funding source: Yunnan Applied Basic Research Projects
Award Identifier / Grant number: 2018FD015
Funding source: the PhD research startup foundation of Yunnan Normal UniversityYunnan Normal UniversityXinyang Normal University
Award Identifier / Grant number: 2016zb012
Award Identifier / Grant number: Unassigned
Award Identifier / Grant number: Unassigned
Acknowledgements
The authors specially thank the referee for many valuable suggestions to revise this paper.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: This work is supported by National Natural Science Foundation of China (No. 11501488), Yunnan Applied Basic Research Projects (No. 2018FD015), Scientific Research Foundation Project of Yunnan Education Department (No. 2018JS150), the PhD research startup foundation of Yunnan Normal University (No. 2016zb012) and Nan Hu Young Scholar Supporting Program of XYNU.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Global stability for a SEIQR worm propagation model in mobile internet
- Study on the coupling calculation model of dump flooding in Hala-hatang fracture-cavity reservoir
- The deterministic and stochastic solutions for the nonlinear Phi-4 equation
- Impacts of heuristic parameters in PSO inverse kinematics solvers
- On separability of non-linear Schrodinger operators with matrix potentials
- General decay projective synchronization of memristive competitive neural networks via nonlinear controller
- Riemann problem and limits of solutions to the isentropic relativistic Euler equations for isothermal gas with flux approximation
- Numerical study of gas–liquid two-phase flow and noise characteristics for a water injection launching concentric canister launcher
- Positivity preserving high order schemes for angiogenesis models
- Numerical study of the energy efficiency of the building envelope containing multi-alveolar structures under Tunisian weather conditions