COMPRESSIBLE NON-ISENTROPIC BIPOLAR NAVIER-STOKES-POISSON SYSTEM IN R3

doi:10.1016/S0252-9602(11)60392-5

Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (6): 2169-2194.doi: 10.1016/S0252-9602(11)60392-5

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COMPRESSIBLE NON-ISENTROPIC BIPOLAR NAVIER-STOKES-POISSON SYSTEM IN R³

Hsiao Ling¹, Li Hailiang², Yang Tong³, Zou Chen⁴

1.Institute of Mathematics, Academy of Mathematics and Systems Science Chinese Academy of Sciences, Beijing 100190, China；2.Department of Mathematics, Capital Normal University, Beijing 100048, China；3.Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China；4.Department of Mechanics and Aerospace Engineering, Peking University, Beijing 100871, China

Received:2011-07-26 Online:2011-11-20 Published:2011-11-20
Supported by:
The research of L. Hsiao was partially supported by the NSFC (10871134). The research of H. Li was partially supported by the NSFC (10871134, 10910401059), and the funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR201006107). The research of T. Yang is supported by the General Research Fund of Hong Kong, City Univ. 103108.

Abstract

Abstract:

The compressible non-isentropic bipolar Navier–Stokes–Poisson (BNSP) sys-tem is investigated in R³ in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in H^l(R³)∩˙B ^−s_1,1(R³) for l ≥4 and s ∈ (0, 1], it is shown that the density and temperature for each charged particle (like electron or ion) decay at the same optimal rate (1 + t)^−3/4 , but the momentum for each particle decays at the optimal rate (1 + t)^−1/4−s/2 which is slower than the rate (1+t^{)−3/4−s/2} for the compressible Navier–Stokes (NS) equations [19] for same initial data. However, the total momentum tends to the constant state at the rate (1+t)^−3/4as well, due to the interplay interaction of charge particles which counteracts the influence of electric field.

Key words: Non-isentropic bipolar Navier-Stokes-Poisson system, optimal time decay rate

Hsiao Ling, Li Hailiang, Yang Tong, Zou Chen. COMPRESSIBLE NON-ISENTROPIC BIPOLAR NAVIER-STOKES-POISSON SYSTEM IN R³[J].Acta mathematica scientia,Series B, 2011, 31(6): 2169-2194.

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COMPRESSIBLE NON-ISENTROPIC BIPOLAR NAVIER-STOKES-POISSON SYSTEM IN R³

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