Boundary layers for a fluid-particle interaction system with density-dependent viscosity and cylindrical symmetry

摘要

In this paper, we study the initial boundary value problem for a cylindrical symmetry fluid-particle interaction system in three dimensions. The boundary layer phenomena is investigated when the shear viscosity mu = kappa rho(beta) goes to zero. Furthermore, we establish the boundary layer thickness of the order O(kappa(alpha)) for more general initial data when 0 < alpha < 1/2 and give the optimal boundary-layer thickness for the system with more general initial data. As a byproduct, this work improves the corresponding results in Yao et al. (2011) for isentropic compressible Navier-Stokes equations where 0 < alpha < 1/4.

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