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Special relativistic effects revealed in the Riemann problem for three-dimensional relativistic Euler equations

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Abstract

We consider the Riemann problem of three-dimensional relativistic Euler equations with two discontinuous initial states separated by a planar hypersurface. Based on the detailed analysis on the Riemann solutions, special relativistic effects are revealed, which are the variations of limiting relative normal velocities and intermediate states and thus the smooth transition of wave patterns when the tangential velocities in the initial states are suitably varied. While in the corresponding non-relativistic fluid, these special relativistic effects will not occur.

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  1. Department of Mathematics, Shanghai Jiao Tong University, 200240, Shanghai, People’s Republic of China

    Yongcai Geng & Yachun Li

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  1. Yongcai Geng
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  2. Yachun Li
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Correspondence to Yachun Li.

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Geng, Y., Li, Y. Special relativistic effects revealed in the Riemann problem for three-dimensional relativistic Euler equations. Z. Angew. Math. Phys. 62, 281–304 (2011). https://doi.org/10.1007/s00033-010-0093-0

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  • DOI: https://doi.org/10.1007/s00033-010-0093-0

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