In this talk I will discuss about compressible Navier-Stokes flows over cut or non-convex domains.

In mechanics, it is very important issue to control the acoustic noises. Such noises may occur at the cut, edge or corner vertices.  We have two critical issues: corner layers, jump discontinuities across the free interface curve.

The pressure gradient in the momentum equations blows up across the streamline emanating from the vertices.

I will discuss about how to handle this issue and will derive the piecewise regularities of the solutions.

Besides, I will introduce some more interesting problems related to this discussions.