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 goes to zero (in fact, in this paper, which implies ) is studied. We prove that the boundary layer thickness is of the order , where for the constant initial data and for the general initial data, which extend the result in Frid and Shelukhin (1999)  to the case of density-dependent viscosity coefficient.
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Lei Yao, Ting Zhang, Changjiang Zhu, Boundary layers for compressible Navier–Stokes equations with density-dependent viscosity and cylindrical symmetry. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 5, pp. 677–709DOI 10.1016/J.ANIHPC.2011.04.006