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

DOI : https://doi.org/10.1016/j.anihpc.2011.04.006
Classification : 76N20,  35B40,  35Q30,  76N10,  76N17
Mots clés : Navier–Stokes equations, Density-dependent viscosity, Cylindrical symmetry, Zero shear viscosity limit, Boundary layers, BL-thickness
@article{AIHPC_2011__28_5_677_0,
author = {Yao, Lei and Zhang, Ting and Zhu, Changjiang},
title = {Boundary layers for compressible Navier{\textendash}Stokes equations with density-dependent viscosity and cylindrical symmetry},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {677--709},
publisher = {Elsevier},
volume = {28},
number = {5},
year = {2011},
doi = {10.1016/j.anihpc.2011.04.006},
zbl = {05965632},
mrnumber = {2838396},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2011.04.006/}
}
Yao, Lei; Zhang, Ting; Zhu, Changjiang. Boundary layers for compressible Navier–Stokes equations with density-dependent viscosity and cylindrical symmetry. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 5, pp. 677-709. doi : 10.1016/j.anihpc.2011.04.006. http://archive.numdam.org/articles/10.1016/j.anihpc.2011.04.006/

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