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

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: $${{\rm {\bf u}}={\rm {\bf w}}+\nabla\varphi_R}$$u=w+∇φR with divw = 0 and a potential $${\varphi_R}$$φR. Here w is the solution for the incompressible Stokes problem and $${\varphi_R}$$φR is defined by subtracting from the solution of the Neumann problem the leading two corner singularities at non-convex vertices.

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