Boundary Layers for the Navier-Stokes Equations of Compressible Heat-Conducting Flows with Cylindrical Symmetry

We consider the Navier-Stokes equations for viscous compressible heat-conducting fluids with cylindrical symmetry. Our main purpose is to study the boundary layer effect and convergence rates as the shear viscosity μ goes to zero. We show that the boundary layer thickness and a convergence rate are of order O(μ) with 0 < α < 1/2 and O( √ μ) respectively, thus extending the result for isentropic flows to non-isentropic flows. As a byproduct, we also improve the convergence result on the vanishing shear viscosity limit. This is joint work with Jianwen Zhang (Xiamen University).