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The main purpose of this paper is to estimate the thickness of boundary layer for nonlinear evolution equations with damping and diffusion as the diffusion parameter β goes to zero. We prove that the thickness of layer is of the order $O(\beta^{\gamma})$ with $0<\gamma<1$ , thus improving the corresponding result in (Ruan and Zhu in Discrete Contin. Dyn. Syst. 32(1) 331-352, 2012) where $0<\gamma<1/2$ is obtained. [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]