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.