For the stationary compressible viscous Navier–Stokes equations with no-slip condition on a convex polygon

Our concern is with existence and regularity of the stationary compressible viscous Navier–Stokes equations with no-slip condition on convex polygonal domains. Note that [u,p]=[0,c], c a constant, is the eigenpair for the singular value λ=1 of the Stokes problem on the convex sector. It is shown that, except the pair [0,c], the leading order of the corner singularities for the nonlinear equations is the same as that of the Stokes problem. We split the leading corner singularity from the solution and show an increased regularity for the remainder. As a consequence the pressure solution changes the sign at the convex corner and its derivatives blow up.