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Asymptotic stability of boundary layer to the multi-dimensional isentropic Euler-Poisson equations arising in plasma physics

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Abstract

This paper is concerned with the initial-boundary value problem on the isentropic Euler-Poisson equations arising in plasma physics in the half space for the spatial dimension \(n=1, 2, 3\). By assuming that the velocity of the positive ion satisfies the Bohm criterion at the far field, we establish the global unique existence and the large time asymptotic stability of boundary layer (i.e., stationary solution) in some weighted Sobolev spaces by weighted energy method. Moreover, the time-decay rates are also obtained.

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Acknowledgements

The authors would like to thank the anonymous referees for the valuable comments and suggestions. The research was supported by the Natural Science Foundation of China \(\#\)12171186, \(\#\)11771169 and the Fundamental Research Funds of the Central Universities \(\#\)CCNU22QN001.

Funding

The research was supported in part by the Natural Science Foundation of China \(\#\)12171186, \(\#\)11771169 and the Fundamental Research Funds of the Central Universities \(\#\)CCNU22QN001.

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Author notes

  1. Yufeng Chen, Wenjuan Ding, Junpei Gao, Mengyuan Lin, and Lizhi Ruan have been contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics and Statistics, and Key Lab NAA–MOE, Central China Normal University, Wuhan, 430079, People’s Republic of China

    Yufeng Chen, Wenjuan Ding, Junpei Gao, Mengyuan Lin & Lizhi Ruan

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  1. Yufeng Chen
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Correspondence to Lizhi Ruan.

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Chen, Y., Ding, W., Gao, J. et al. Asymptotic stability of boundary layer to the multi-dimensional isentropic Euler-Poisson equations arising in plasma physics. Calc. Var. 63, 71 (2024). https://doi.org/10.1007/s00526-024-02680-1

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