摘要
We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation.If the Fourier modes of the initial data are degenerate at the low frequency or the initial data decay fast at spatial infinity,we show that the density converges to its equilibrium state at the L 2-rate (1+t)(-7/4) or L ∞-rate (1+t)(-5/2),and the momentum decays at the L 2-rate (1+t)(-5/4) or L ∞-rate (1+t)(-2).These convergence rates are shown to be optimal for the compressible Navier-Stokes-Poisson system.
We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation. If the Fourier modes of the initial data are degenerate at the low frequency or the initial data decay fast at spatial infinity, we show that the density converges to its equilibrium state at the L2-rate （1 ＋t）- 7/4 or L∞-rate （1 ＋t）- 5/2, and the momentum decays at the L2-rate （1 ＋t）-5/4 or L∞-rate （1 ＋ t）-2. These convergence rates are shown to be optimal for the compressible Navier-Stokes-Poisson system.
基金
partially supported by National Natural Science Foundation of China(Grant Nos.10871134,11011130029)
the Huo Ying Dong Foundation (Grant No.111033)
the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (Grant No.PHR201006107)
partially supported by National Natural Science Foundation of China (Grant Nos.10871175,10931007,10901137)
Zhejiang Provincial Natural Science Foundation of China (Grant No.Z6100217)
Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20090101120005)
