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

doi:10.1016/S0252-9602(11)60357-3

Abstract

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 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.

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

CLC Number:

35B40

ZOU Chen. LARGE TIME BEHAVIORS OF THE ISENTROPIC BIPOLAR COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM[J].Acta mathematica scientia,Series B, 2011, 31(5): 1725-1740.

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