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 μ=ϵρ θ goes to zero (in fact, ϵ0 in this paper, which implies μ0) is studied. We prove that the boundary layer thickness is of the order O(ϵ α ), where 0<α<1 2 for the constant initial data and 0<α<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 : 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
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     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},
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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://www.numdam.org/articles/10.1016/j.anihpc.2011.04.006/

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