数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (5): 1725-1740.doi: 10.1016/S0252-9602(11)60357-3

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LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

邹晨   

  1. Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, China
  • 收稿日期:2010-07-05 出版日期:2011-09-20 发布日期:2011-09-20
  • 基金资助:

    This research is partially supported by NSFC (10872004), National Basic Research Program of China (2010CB731500), and the China Ministry of Education (200800010013).

LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

 ZOU Chen   

  1. Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, China
  • Received:2010-07-05 Online:2011-09-20 Published:2011-09-20
  • Supported by:

    This research is partially supported by NSFC (10872004), National Basic Research Program of China (2010CB731500), and the China Ministry of Education (200800010013).

摘要:

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 Hl(R3)∩˙Bs1,1(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

Abstract:

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 Hl(R3)∩˙Bs1,1(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.

Key words: bipolar Navier-Stokes-Poisson system, optimal time convergence rate, total momentum

中图分类号: 

  • 35B40