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Abstract: In this paper, the compressible non-isentropic Navier–Stokes–Poisson (NSP) system is considered in 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 as the non-isentropic compressible Navier–Stokes system, but the momentum decays at the rate , which is slower than the rate for the pure compressible Navier–Stokes system. These convergence rates are also shown to be optimal for the non-isentropic compressible NSP system. [Copyright &y& Elsevier]

Abstract: The dynamical behaviors of vacuum states for one-dimensional compressible Navier–Stokes equations with density-dependent viscosity coefficient are considered. It is first shown that a unique strong solution to the free boundary value problem exists globally in time, the free boundary expands outwards at an algebraic rate in time, and the density is strictly positive in any finite time but decays pointwise to zero time-asymptotically. Then, it is proved that there exists a unique global weak solution to the initial boundary value problem when the initial data contains discontinuously a piece of continuous vacuum and is regular away from the vacuum. The solution is piecewise regular and contains a piece of continuous vacuum before the time , which is compressed at an algebraic rate and vanishes at the time , meanwhile the weak solution becomes either a strong solution or a piecewise strong one and tends to the equilibrium state exponentially. [Copyright &y& Elsevier]