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Singular limits for the Navier-Stokes-Poisson equations of the viscous plasma with the strong density boundary layer

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Abstract

The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space \(\mathbb{R}_+^3\) is rigorously proved under a Navier-slip boundary condition for velocity and the Dirichlet boundary condition for electric potential. This is achieved by establishing the nonlinear stability of the approximation solutions involving the strong boundary layer in density and electric potential, which comes from the breakdown of the quasi-neutrality near the boundary, and dealing with the difficulty of the interaction of this strong boundary layer with the weak boundary layer of the velocity field.

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Acknowledgements

Qiangchang Ju was supported by National Natural Science Foundation of China (Grant Nos. 12131007 and 12070144). Tao Luo was supported by a General Research Fund of Research Grants Council (Hong Kong) (Grant No. 11306117). Xin Xu was supported by National Natural Science Foundation of China (Grant No. 12001506) and Natural Science Foundation of Shandong Province (Grant No. ZR2020QA014). The work of Qiangchang Ju and Xin Xu was supported by the Israel Science Foundation-National Natural Science Foundation of China Joint Research Program (Grant No. 11761141008).

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Authors and Affiliations

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

    Qiangchang Ju

  2. Department of Mathematics, City University of Hong Kong, Hong Kong, China

    Tao Luo

  3. School of Mathematical Sciences and College of Oceanic and Atmospheric Sciences, Ocean University of China, Qingdao, 266100, China

    Xin Xu

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  1. Qiangchang Ju
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  2. Tao Luo
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  3. Xin Xu
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Correspondence to Xin Xu.

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Ju, Q., Luo, T. & Xu, X. Singular limits for the Navier-Stokes-Poisson equations of the viscous plasma with the strong density boundary layer. Sci. China Math. 66, 1495–1528 (2023). https://doi.org/10.1007/s11425-022-2008-8

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  • DOI: https://doi.org/10.1007/s11425-022-2008-8

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