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

### Lei Yao

Department of Mathematics, Northwest University, Xiʼan 710127, China### Ting Zhang

Department of Mathematics, Zhejiang University, Hangzhou 310027, China### Changjiang Zhu

The Hubei Key Laboratory of Mathematical Physics, School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

## 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 $μ=ερ_{θ}$ 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 $O(ε_{α})$, where $0<α<21 $ for the constant initial data and $0<α<41 $ for the general initial data, which extend the result in Frid and Shelukhin (1999) [4] to the case of density-dependent viscosity coefficient.

## Cite this article

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. 677–709

DOI 10.1016/J.ANIHPC.2011.04.006