Boundary layers for compressible Navier–Stokes equations with density-dependent viscosity and cylindrical symmetry

In this paper, we consider the zero shear viscosity limit for the Navier–Stokes equations of compressible flows with density-dependent viscosity coefficient and cylindrical symmetry. The boundary layer effect as the shear viscosity μ=ερθ goes to zero (in fact, ε→0 in this paper, which implies μ→0) is studied. We prove that the boundary layer thickness is of the order O(εα), where for the constant initial data and for the general initial data, which extend the result in Frid and Shelukhin (1999) [4] to the case of density-dependent viscosity coefficient.