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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 global in-time semiclassical and relaxation limits of the bipolar quantum hydrodynamic model for semiconductors are investigated in . We prove that the unique strong solution exists and converges globally in time to the strong solution of classical bipolar hydrodynamical equation in the process of semiclassical limit and that of the classical drift–diffusion system under the combined relaxation and semiclassical limits. [Copyright &y& Elsevier]

The initial boundary value problem for the compressible barotropic Navier–Stokes equations is investigated in the case that the initial density has a jump discontinuity across an interior closed curve in two-dimensional bounded domain. If the initial data is a small perturbation of the constant state and the interior closed curve is near a circle inside the domain, the global existence and large time behavior of the piecewise strong solution is shown, in particular, the jump of the fluid density across the convecting curve decays exponentially in time. [ABSTRACT FROM AUTHOR]