Boundary layers for compressible Navier¨CStokes equations with density-dependent viscosity and cylindrical symmetry

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• 作者：Lei  ; Yao^a ;   ; ^{yaolei1056@hotmail.com} ; Ting  ; Zhang^b ;   ; ^{zhangting79@zju.edu.cn} ; Changjiang  ; Zhu^c ;   ; ^{cjzhu@mail.ccnu.edu.cn}
• 关键词：Navier&ndash ; Stokes equations ; Density-dependent viscosity ; Cylindrical symmetry ; Zero shear viscosity limit ; Boundary layers ; BL-thickness
• 刊名：Annales de l'Institut Henri Poincare (C) Non Linear Analysis
• 出版年：2011
• 出版时间：September-October 2011
• 年：2011
• 卷：28
• 期：5
• 页码：677-709
• 全文大小：292 K

文摘

In this paper, we consider the zero shear viscosity limit for the Navier¨CStokes 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.