Time asymptotic behavior of the bipolar Navier-Stokes-Poisson system

Hai-Liang Li Tong Yang Chen Zou

Analysis of PDEs mathscidoc:1912.43950

Acta Mathematica Scientia, 29, (6), 1721-1736, 2009.11
Abstract The bipolar Navier-Stokes-Poisson system (BNSP) has been used to simulate the transport of charged particles (ions and electrons for instance) under the influence of electrostatic force governed by the self-consistent Poisson equation. The optimal L 2 time convergence rate for the global classical solution is obtained for a small initial perturbation of the constant equilibrium state. It is shown that due to the electric field, the difference of the charge densities tend to the equilibrium states at the optimal rate (1+ t)-3 4 in L 2-norm, while the individual momentum of the charged particles converges at the optimal rate (1+ t)-1 4 which is slower than the rate (1+ t)-3 4 for the compressible Navier-Stokes equations (NS). In addition, a new phenomenon on the charge transport is observed regarding the interplay between the two carriers that almost counteracts the influence of the electric field so that the total density and
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  title={Time asymptotic behavior of the bipolar Navier-Stokes-Poisson system},
  author={Hai-Liang Li, Tong Yang, and Chen Zou},
  booktitle={Acta Mathematica Scientia},
Hai-Liang Li, Tong Yang, and Chen Zou. Time asymptotic behavior of the bipolar Navier-Stokes-Poisson system. 2009. Vol. 29. In Acta Mathematica Scientia. pp.1721-1736. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210848757496514.
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