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

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

44 Scopus Citations
View graph of relations

Author(s)

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)1721-1736
Journal / PublicationActa Mathematica Scientia
Volume29
Issue number6
Publication statusPublished - Nov 2009

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 L2 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)- frac(3, 4) in L2-norm, while the individual momentum of the charged particles converges at the optimal rate (1 + t)- frac(1, 4) which is slower than the rate (1 + t)- frac(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 momentum of the two carriers converges at a faster rate (1 + t)- frac(3, 4) + ε for any small constant ε > 0. The above estimates reveal the essential difference between the unipolar and the bipolar Navier-Stokes-Poisson systems. © 2009 Wuhan Institute of Physics and Mathematics.

Research Area(s)

  • 35B40, 35Q15, 76X05, bipolar Navier-Stokes-Poisson system, optimal time convergence rate, spectrum analysis, total momentum

Citation Format(s)

Time asymptotic behavior of the bipolar Navier-Stokes-Poisson system. / Li, Hai-Liang; Yang, Tong; Zou, Chen.
In: Acta Mathematica Scientia, Vol. 29, No. 6, 11.2009, p. 1721-1736.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review