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Self-similar solutions of the radially symmetric relativistic Euler equations

Part of: Hyperbolic equations and systems

Published online by Cambridge University Press:  04 November 2019

GENG LAI Open the ORCID record for GENG LAI [Opens in a new window]
GENG LAI*
Affiliation:
Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China email: laigeng@shu.edu.cn
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Abstract

The study of radially symmetric motion is important for the theory of explosion waves. We construct rigorously self-similar entropy solutions to Riemann initial-boundary value problems for the radially symmetric relativistic Euler equations. We use the assumption of self-similarity to reduce the relativistic Euler equations to a system of nonlinear ordinary differential equations, from which we obtain detailed structures of solutions besides their existence. For the ultra-relativistic Euler equations, we also obtain the uniqueness of the self-similar entropy solution to the Riemann initial-boundary value problems.

Keywords

Relativistic Euler equationsradial symmetryRiemann problemself-similar solution

MSC classification

Primary: 35L65: Conservation laws
Secondary: 35L60: Nonlinear first-order hyperbolic equations 35L67: Shocks and singularities
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 6 , December 2020 , pp. 919 - 949
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Copyright
© Cambridge University Press 2019

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Footnotes

†

This work was partially supported by NSF of China 11301326 and the grant of ‘Shanghai Altitude Discipline’.

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