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Nonrelativistic limits for the 1D relativistic Euler equations with physical vacuum

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Abstract

We prove the nonrelativistic limits of the local smooth solutions to the free boundary value problem of the 1D relativistic Euler equations, when the mass energy density includes the vacuum states at the free boundary. We successfully overcome the strong nonlinearity and the degenerate difficulty of the relativistic Euler equations caused by the Lorentz factor and the vacuum occurring on the moving boundary, respectively. Moreover, the smooth solutions of the relativistic Euler equations converge to the solutions of the classical compressible Euler equation, at the rate of \(\frac{1}{c^2}\).

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Acknowledgements

Our work is partially supported by the National Natural Science Foundation of China (Nos. 11601246, 11971014) and the Program of Higher Level talents of Inner Mongolia University (No. 21100-5165105).

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  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, China

    La-Su Mai & Xiaoting Cao

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  1. La-Su Mai
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Correspondence to La-Su Mai.

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Mai, LS., Cao, X. Nonrelativistic limits for the 1D relativistic Euler equations with physical vacuum. Z. Angew. Math. Phys. 70, 145 (2019). https://doi.org/10.1007/s00033-019-1189-9

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  • DOI: https://doi.org/10.1007/s00033-019-1189-9

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