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

Abstract

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.