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Global symmetric solutions for a multi-dimensional compressible viscous gas with radiation in exterior domains

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Abstract

This paper is devoted to the study of the initial-boundary value problem for a multi-dimensional compressible Navier–Stokes–Poisson coupled system that describes the motion of a viscous gas with radiation, in the domain exterior to a ball of \(\mathbb {R}^d\). By means of nonlinear energy method, we show the global-in-time existence and asymptotic stability of the spherically and cylindrically symmetric solutions for large initial data, provided that the adiabatic exponent \(\gamma \) is sufficiently close to 1.

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Acknowledgements

The research of Ling Wan was supported in part by the grant from National Natural Science Foundation of China (Contract No. 11801530) and the Fundamental Research Funds for the Central Universities (Contract No. CUG170674). The authors express much gratitude to Professor Huijiang Zhao for his support and advice.

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Authors and Affiliations

  1. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China

    Ling Wan

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Lin-Xia Wu

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  1. Ling Wan
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  2. Lin-Xia Wu
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Correspondence to Ling Wan.

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Wan, L., Wu, LX. Global symmetric solutions for a multi-dimensional compressible viscous gas with radiation in exterior domains. Z. Angew. Math. Phys. 70, 130 (2019). https://doi.org/10.1007/s00033-019-1171-6

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  • DOI: https://doi.org/10.1007/s00033-019-1171-6

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