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

Abstract

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 μ=κρβ goes to zero. Furthermore, we establish the boundary layer thickness of the order O(κα) for more general initial data when 0<α<12 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<α<14.