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We study an ocean related system with a small viscosity parameter, which is the linearized version of the modified Primitive Equations. As the parameter goes to zero, a L ∞ convergence result is obtained together with the estimation on the thickness of the boundary layer. [ABSTRACT FROM AUTHOR]

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]

Both the global well-posedness for large data and the vanishing shear viscosity limit with a boundary layer to the compressible Navier-Stokes system with cylindrical symmetry are studied under a general condition on the heat conductivity coefficient that, in particular, includes the constant coefficient. The thickness of the boundary layer is proved to be almost optimal. Moreover, the optimal L convergence rate in terms of shear viscosity is obtained for the angular and axial velocity components. [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]