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

Yao, Lei; Zhang, Ting; Zhu, Changjiang

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 5, pp. 677-709

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 $\mu =ϵ{\rho }^{\theta }$ goes to zero (in fact, $ϵ\to 0$ in this paper, which implies $\mu \to 0$) is studied. We prove that the boundary layer thickness is of the order $O\left({ϵ}^{\alpha }\right)$, 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.

Classification : 76N20, 35B40, 35Q30, 76N10, 76N17
Keywords: Navier–Stokes equations, Density-dependent viscosity, Cylindrical symmetry, Zero shear viscosity limit, Boundary layers, BL-thickness

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