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Global symmetric solutions of compressible Navier–Stokes equations for a reacting mixture in unbounded domains

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Abstract

We consider the compressible Navier–Stokes equations for a reacting mixture describing the dynamic combustion in multidimensional unbounded domains. We prove the global existence, uniqueness, and large-time asymptotic behavior of spherically and cylindrically symmetric solutions with large initial data. The key point in the proof is to establish uniform-in-time bounds for the specific volume and temperature. Several new estimates are derived in order to handle the reacting terms and the unboundedness of the domain.

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Acknowledgements

The research was supported in part by the National Natural Science Foundation of China (No. 12371228), and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan).

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

    Ling Wan & Teng-Fei Zhang

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  1. Ling Wan
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Wan, L., Zhang, TF. Global symmetric solutions of compressible Navier–Stokes equations for a reacting mixture in unbounded domains. Z. Angew. Math. Phys. 74, 244 (2023). https://doi.org/10.1007/s00033-023-02136-0

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