Compressible viscous Navier-Stokes flows: Corner singularity, regularity
2013. 03. 28.
In this talk I will talk about existence and regularity for solutions
to the compressible viscous Navier-Stokes equations on nonsmooth domains,
especially with corners. The solution is constructed by the decomposition
of the corner singularities and the regular part. An increased regularity
for the remainder and the density function is shown. The singularity
is propagated into the region by the transport character of the continuity
equation. One may have applications in describing the propagation into
the region of the local sound wave impact occured at corners and a damage
to the body domain by the singular boundary.