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 $\mu =\epsilon {\rho }^{\theta }$ goes to zero (in fact, $\epsilon \to 0$ in this paper, which implies $\mu \to 0$) is studied. We prove that the boundary layer thickness is of the order $O({\epsilon }^{\alpha })$, where $0<\alpha <\frac{1}{2}$ for the constant initial data and $0<\alpha <\frac{1}{4}$ for the general initial data, which extend the result in Frid and Shelukhin (1999) [4] to the case of density-dependent viscosity coefficient.