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

Abstract

We consider the Navier–Stokes equations of viscous compressible heat-conducting flows with cylindrical symmetry. Our main purpose is to study the boundary layer effect and the convergence rate as the shear viscosity $\mu$ goes to zero. We show that the boundary layer thickness and a convergence rate are of the orders $O(\mu^\alpha)$ with $0<\alpha<1/2$ and $O(\sqrt{\mu})$, respectively, thus extending the result in [H. Frid and V. V. Shelukhin, Commun. Math. Phys., 208 (1999), pp. 309–330] to the case of nonisentropic flows. As a byproduct, we also improve the convergence result in [H. Frid and V. V. Shelukhin, SIAM J. Math. Anal., 31 (2000), pp. 1144–1156] on the vanishing shear viscosity limit.