Large time behavior of solutions to 3D compressible Navier-Stokes-Poisson system  

作　　者：LI HaiLiang ZHANG Ting 

机构地区：[1]Department of Mathematics and Institute of Mathematics and Interdisciplinary Science,Capital Normal University,Beijing 100048,China [2]Department of Mathematics,Zhejiang University,Hangzhou 310027,China

出　　处：《Science China Mathematics》2012年第1期159-177,共19页中国科学：数学（英文版）

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)

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.

关 键 词：compressible Navier-Stokes-Poisson system optimal decay rate 

分 类 号：O175.8[理学—数学] TE357.4[理学—基础数学]