Optimal decay rate of the non-isentropic compressible Navier-Stokes-Poisson system in R3

In this paper, the compressible non-isentropic Navier-Stokes-Poisson (NSP) system is considered in R-3 and the influences of internal electric field on the qualitative behaviors of solutions are analyzed. We observe that the electric field leads to the rotating phenomena in charge transport and reduces the speed of fluid motion, but it does not influence the transport of charge density and the heat diffusion. Indeed, we show that both density and temperature of the NSP system converge to their equilibrium state at the same rate (1 + t)(-3/4) as the non-isentropic compressible Navier-Stokes system, but the momentum decays at the rate (1 + t)(-1/4) A. which is slower than the rate (1 + t)(-3/4) for the pure compressible Navier-Stokes system. These convergence rates are also shown to be optimal for the non-isentropic compressible NSP system. (C) 2010 Elsevier Inc. All rights reserved.