Singularities in the Density Gradient

The compressible steady state Navier–Stokes system with viscosity is considered on a plane polygonal domain. It is shown that if a solution satisfies certain reasonable regularity conditions, and if the velocity is non-zero and points into the domain at a vertex of the polygon, then the gradient of the density either becomes infinite or has a jump discontinuity at each point of the streamline emanating from the vertex.