In this paper we consider the initial-boundary value problem to the one-dimensional compressible Navier{Stokes equations for ideal gases. Both the viscous and heat conductive coeffcients are assumed to be positive constants, and the initial density is allowed to have vacuum. Global existence and uniqueness of strong solutions is established for any H2 initial data, which generalizes the well-known result of Kazhikhov and Shelukhin [J. Appl. Math. Mech., 41 (1977), pp. 273{282] to the case that with nonnegative initial density. An observation to overcome the diculty caused by the lack of the positive lower bound of the density is that the ratio of the density to its initial value is inversely proportional to the time integral of the upper bound of the temperature along the trajectory.

The inflow problem of full compressible NavierStokes equations is considered on the half-line (0,+\infty). First, we give the existence (or nonexistence) of the boundary layer solution to the inflow problem when the right end state (0,+\infty) belongs to the subsonic, transonic, and supersonic regions, respectively. Then the asymptotic stability of not only the single contact wave but also the superposition of the subsonic boundary layer solution, the contact wave, and the rarefaction wave to the inflow problem are investigated under some smallness conditions. Note that the amplitude of the rarefaction wave is not necessarily small. The proofs are given by the elementary energy method.

We establish local higher integrability estimates for upper gradients of vector-valued parabolic quasi-minimizers in metric measure spaces, satisfying a doubling property and supporting a weak Poincaré inequality.

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where p > 1. 1 < p < 2 is called the fast p-Laplacian diffusion, while p > 2 is called the slow p-Laplacian diffusion. Especially, the p-Laplacian Keller-Segel model turns to the original model when p = 2.The Keller-Segel model was firstly presented in 1970 to describe the chemotaxis of cellular slime molds [13, 14]. The original model was considered in 2D,