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Convergence of the Navier–Stokes–Maxwell system to the Euler–Maxwell system near constant equilibrium

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Abstract

The aim of this paper is to provide a justification of the vanishing viscosity limit of the compressible Navier–Stokes–Maxwell system in the whole space. With suitable initial data, we rigorously prove that there exists a sequence of unique smooth solutions of the Navier–Stokes–Maxwell system which converges to the given smooth solution of the Euler–Maxwell system near constant equilibrium when the viscosity coefficients tend to zero. Moreover, a uniform convergence rate is obtained in terms of the viscosity coefficients. As a byproduct, a similar result for the compressible Navier–Stokes–Poisson system is also obtained.

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Acknowledgements

The research of Zongguang Li is supported by the Hong Kong PhD Fellowship Scheme. Zongguang Li would like to thank Professor Renjun Duan for his support during the PhD studies in the Chinese University of Hong Kong. Dongcheng Yang would like to thank Department of Mathematics, CUHK for hosting his visit in the period 2020–2023.

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  1. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, People’s Republic of China

    Zongguang Li & Dongcheng Yang

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  1. Zongguang Li
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Li, Z., Yang, D. Convergence of the Navier–Stokes–Maxwell system to the Euler–Maxwell system near constant equilibrium. Z. Angew. Math. Phys. 74, 108 (2023). https://doi.org/10.1007/s00033-023-02000-1

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  • DOI: https://doi.org/10.1007/s00033-023-02000-1

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