Vanishing Shear Viscosity and Boundary Layer for the Navier–Stokes Equations with Cylindrical Symmetry

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 L¹ convergence rate in terms of shear viscosity is obtained for the angular and axial velocity components.