On the non-isentropic compressible Navier–Stokes equations with cylindrical symmetry: boundary layers and convergence rate at vanishing shear viscosity

We consider the initial-boundary value problem for the non-isentropic compressible Navier–Stokes equations with cylindrical symmetry in three dimensions. It is well known that boundary layers present when the shear viscosity vanishes. In this paper, we derive the explicit boundary layer equations of Prandtl type for each boundary with heat conductivity coefficient dependent on temperature or as a constant. Furthermore, we improve the convergence rate of the vanishing shear viscosity to O(ϵ516)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal {O}(\epsilon ^{\frac{5}{16}}) $$\end{document} without any smallness assumptions for the initial and boundary data.