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

Qiangchang Ju; Tao Luo; Xin Xu

doi:10.1007/s11425-022-2008-8

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

Qiangchang Ju, Tao Luo, Xin Xu^*

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

3 Citations (Scopus)

28 Downloads (CityUHK Scholars)

Abstract

The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space 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. © 2023, Science China Press.

Original language	English
Pages (from-to)	1495–1528
Number of pages	34
Journal	Science China Mathematics
Volume	66
Issue number	7
Online published	8 Feb 2023
DOIs	https://doi.org/10.1007/s11425-022-2008-8
Publication status	Published - Jul 2023

Funding

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).

Research Keywords

interaction of strong and weak boundary layers
Navier-Stokes-Poisson equations
singular limit

Publisher's Copyright Statement

COPYRIGHT TERMS OF DEPOSITED POSTPRINT FILE: This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s11425-022-2008-8.

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

abstract = "The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space 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. {\textcopyright} 2023, Science China Press.",

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author = "Qiangchang Ju and Tao Luo and Xin Xu",

year = "2023",

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AU - Ju, Qiangchang

AU - Luo, Tao

AU - Xu, Xin

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Y1 - 2023/7

N2 - The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space 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. © 2023, Science China Press.

AB - The quasi-neutral limit of the Navier-Stokes-Poisson system modeling a viscous plasma with vanishing viscosity coefficients in the half-space 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. © 2023, Science China Press.

KW - interaction of strong and weak boundary layers

KW - Navier-Stokes-Poisson equations

KW - singular limit

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DO - 10.1007/s11425-022-2008-8

M3 - RGC 21 - Publication in refereed journal

SN - 1674-7283

VL - 66

SP - 1495

EP - 1528

JO - Science China Mathematics

JF - Science China Mathematics

IS - 7

ER -

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

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GRF: Qualitative Analysis for a System of Hyperbolic Partial Differential Equations of Conservation Laws in the Presence of Physical Boundaries and Initial Layers

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

Abstract

Funding

Research Keywords

Publisher's Copyright Statement

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

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GRF: Qualitative Analysis for a System of Hyperbolic Partial Differential Equations of Conservation Laws in the Presence of Physical Boundaries and Initial Layers

Cite this