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

Yao, Lei; Zhang, Ting; Zhu, Changjiang

Yao, Lei ; Zhang, Ting ; Zhu, Changjiang

Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011), p. 677-709 / Harvested from Numdam

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Résumé

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 $μ = ϵ ρ^{θ}$ goes to zero (in fact, $ϵ \to 0$ in this paper, which implies $μ \to 0$ ) is studied. We prove that the boundary layer thickness is of the order $O (ϵ^{α})$ , where $0 < α < \frac{1}{2}$ for the constant initial data and $0 < α < \frac{1}{4}$ for the general initial data, which extend the result in Frid and Shelukhin (1999) [4] to the case of density-dependent viscosity coefficient.

Publié le : 2011-01-01

MR 2838396 | Zbl 05965632

DOI : https://doi.org/10.1016/j.anihpc.2011.04.006
Classification: 76N20, 35B40, 35Q30, 76N10, 76N17

@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},
     volume = {28},
     year = {2011},
     pages = {677-709},
     doi = {10.1016/j.anihpc.2011.04.006},
     mrnumber = {2838396},
     zbl = {05965632},
     language = {en},
     url = {http://dml.mathdoc.fr/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, Tome 28 (2011) pp. 677-709. doi : 10.1016/j.anihpc.2011.04.006. http://gdmltest.u-ga.fr/item/AIHPC_2011__28_5_677_0/

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