Compressible Navier-Stokes Equations in a Polyhedral Cylinder with Inflow Boundary Condition

Abstract

In this paper our concern is with singularity and regularity of the compressible flows through a non-convex edge in R-3. The flows are governed by the compressible Navies-Stokes equations on the infinite cylinder that has the non-convex edge on the inflow boundary. We split the edge singularity by the Poisson problem from the velocity vector and show that the remainder is twice differentiable while the edge singularity is observed to be propagated into the interior of the cylinder by the transport character of the continuity equation. An interior surface layer starting at the edge is generated and not Lipshitz continuous due to the singularity. The density function shows a very steep change near the interface and its normal derivative has a jump discontinuity across there.