Stability of Boundary Layers for the Nonisentropic Compressible Circularly Symmetric 2D Flow

In this paper, we study the asymptotic behavior of the circularly symmetric solution to the initial boundary value problem of the compressible non-isentropic Navier-Stokes equations in a two-dimensional exterior domain with impermeable boundary condition when the viscosities and the heat conduction coefficient tend to zero. By multi-scale analysis, we obtain that away from the boundary the compressible nonisentropic viscous flow can be approximated by the corresponding inviscid flow, and near the boundary there are boundary layers for the angular velocity, density and temperature in the leading order expansions of solutions, while the radial velocity and pressure do not have boundary layers in the leading order. The boundary layers of velocity and temperature are described by a nonlinear parabolic coupled system. We prove the stability of boundary layers and rigorously justify the asymptotic behavior of solutions in the L∞−norm for the small viscosities and heat-conduction limit in the Lagrangian coordinates, as long as the strength of the boundary layers is suitably small. Finally, we show that the similar asymptotic behavior of the small viscosities and heat conduction limit holds in the Eulerian coordinates for the compressible non-isentropic viscous flow.