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QUASI-NEUTRAL LIMIT OF THE bipolar navier-stokes-poisson system

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Acta Mathematica Scientia 2011年第4期31卷 1272-1280页

作者：杨秀绘 Department of Mathematics College of Science Nanjing University of Aeronautics and Astronautics

This paper is concerned with the quasi-neutral limit of the bipolar navierstokes-poisson system. It is rigorously proved, by introducing the new modulated energy functional and using the refined energy analysis, that the strong solutions of the bipolar navier-stokes-poisson system converge to the strong solution of the compressible navierstokes equations as the Debye length goes to zero. Moreover, if we let the viscous coefficients and the Debye length go to zero simultaneously, then we obtain the convergence of the strong solutions of bipolar navier-stokes-poisson system to the strong solution of the compressible Euler equations.

关键词： bipolar navier-stokes-poisson system compressible navier-stokes equations compressible Euler equations modulated energy functional

TIME ASYMPTOTIC BEHAVIOR OF THE bipolar navier-stokes-poisson system

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Acta Mathematica Scientia 2009年第6期29卷 1721-1736页

作者： Hai-Liang Li Tong Yang Chen Zou Department of Mathematics Capital Normal University Beijing 100048 China Department of Mathematics City University of Hong Kong 83 Tat Chee Avenue Kowloon Hong Kong Department of Mechanics and Aerospace Engineering COE Peking University Beijing 100871 China

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 momentum of the two carriers converges at a faster rate （1 ＋ t）^-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.

关键词： bipolar navier-stokes-poisson system optimal time convergence rate spectrum analysis total momentum

LARGE TIME BEHAVIORS OF THE ISENTROPIC bipolar COMPRESSIBLE navier-stokes-poisson system

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Acta Mathematica Scientia 2011年第5期31卷 1725-1740页

作者：邹晨 Department of Mechanics and Aerospace Engineering Peking University

The isentropic bipolar compressible navier-stokes-poisson （BNSP） system is investigated in R3 in the present paper. The optimal time decay rate of global strong solution is established. When the regular initial data belong to the Sobolev space H l（R3） ∩ B˙ s 1,1 （R3） with l ≥ 4 and s ∈ （0, 1], it is shown that the momenta of the charged particles decay at the optimal rate （1＋t） 1 4 s 2 in L2 -norm, which is slower than the rate （1＋t） 3 4 s 2 for the compressible navier-stokes （NS） equations [14]. In particular, a new phenomenon on the charge transport is observed. The time decay rate of total density and momentum was both （1 ＋ t） 3 4 due to the cancellation effect from the interplay interaction of the charged particles.

关键词： bipolar navier-stokes-poisson system optimal time convergence rate total momentum