The Compressible Stokes Flows with No-Slip Boundary Condition on Non-convex Polygons

Abstract

In this paper we study the compressible Stokes equations with no-slip boundary condition on non-convex polygons and show a best regularity result that the solution can have without subtracting corner singularities. This is obtained by a suitable Helmholtz decomposition: u = w + del phi R with divw = 0 and a potential phi R. Here w is the solution for the incompressible Stokes problem and phi R is defined by subtracting from the solution of the Neumann problem the leading two corner singularities at non-convex vertices.