A regularity result of solution to the compressible Stokes equations on a convex polygon

A compressible Stokes problem is analyzed in a convexpolygon D. The goal of this paper is to sort out a singularityof the pressure function at the corner and to establish thecorresponding regularity result of the resulted remainder part ofthe solution. For this a solution formula is derived and thesingular function of the Stokes problem is considered. It is seenthat the lowest order of the regularity of the system is the sameas that of the (incompressible) Stokes one.