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

Abstract

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 0<α<12 for the constant initial data and 0<α<14 for the general initial data, which extend the result in Frid and Shelukhin (1999) [4] to the case of density-dependent viscosity coefficient.