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We consider an initial boundary problem for the planar MHD system under the general condition on the heat conductivity coefficient that depends on both the temperature and the density. Firstly, the global existence of strong solution for large initial data is obtained, and then the limit of the vanishing shear viscosity is justified. In addition, the L 2 convergence rate is obtained together with the estimation on the thickness of the boundary layer. [ABSTRACT FROM AUTHOR]

The existence of global solutions is established for compressible Navier-Stokes equations by taking into account the radiative and reactive processes, when the heat conductivity κ ( κ1(1 + θ q) ≤ κ ≤ κ2(1 + θ q), q ≥ 0), where θ is the temperature. This improves the previous results by enlarging the scope of q including the constant heat conductivity. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: A mathematical model for viscous, real, compressible, reactive fluid flows is considered. The existence of global solutions for the free boundary problem with species diffusion in dynamic combustion is established when the viscosity λ depends on the density i.e., (), where A is a generic positive constant. Furthermore, the equations of state depend nonlinearly on density and temperature unlike the case of perfect gases or radiative flows. In addition, the shock wave, turbulence, vacuum, mass concentration or extremely hot spot will not be developed in any finite time if the initial data do not contain vacuum. [Copyright &y& Elsevier]

Abstract: In this paper we study a free boundary problem for the viscous, compressible, heat conducting, one-dimensional real fluids. More precisely, the viscosity is assumed to be a power function of density, i.e., , where ρ denotes the density of fluids and α is a positive constant. In addition, the equations of state include and are more general than perfect flows which only depend linearly on temperature. The global existence (uniqueness) of smooth solutions is established with for general, large initial data, which improves the previous results. Moreover, it is also shown that the solutions will not develop vacuum, mass concentration or heat concentration in a finite time provided the initial data are bounded and smooth, and do not contain vacuum. [Copyright &y& Elsevier]