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Remarks on the Cauchy problem of the one-dimensional viscous radiative and reactive gas

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Abstract

This paper is concerned with the large-time behavior of solutions to the Cauchy problem of a one-dimensional viscous radiative and reactive gas. Based on the elaborate energy estimates, we develop a new approach to derive the upper bound of the absolute temperature by avoiding the use of auxiliary functions Z(t) and W(t) introduced by Liao and Zhao [J. Differential Equations, 2018, 265(5): 2076–2120]. Our results also improve upon the results obtained in Liao and Zhao [J. Differential Equations, 2018, 265(5): 2076–2120].

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Acknowledgements

The author expresses much gratitude to Professor Huijiang Zhao for his support and advice.

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Yongkai Liao

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  1. Yongkai Liao
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Correspondence to Yongkai Liao.

Additional information

The research was supported by National Postdoctoral Program for Innovative Talents of China (BX20180054).

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Liao, Y. Remarks on the Cauchy problem of the one-dimensional viscous radiative and reactive gas. Acta Math Sci 40, 1020–1034 (2020). https://doi.org/10.1007/s10473-020-0410-4

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  • DOI: https://doi.org/10.1007/s10473-020-0410-4

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