Boundary layers for compressible Navier–Stokes equations with density-dependent viscosity and cylindrical symmetry
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 5, p. 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 : https://doi.org/10.1016/j.anihpc.2011.04.006
Classification:  76N20,  35B40,  35Q30,  76N10,  76N17
Keywords: 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--Stokes equations with density-dependent viscosity and cylindrical symmetry},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {28},
     number = {5},
     year = {2011},
     pages = {677-709},
     doi = {10.1016/j.anihpc.2011.04.006},
     zbl = {05965632},
     mrnumber = {2838396},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2011__28_5_677_0}
}
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, Volume 28 (2011) no. 5, pp. 677-709. doi : 10.1016/j.anihpc.2011.04.006. http://www.numdam.org/item/AIHPC_2011__28_5_677_0/

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