An Explicit Formula for Corner Singularity Expansion of the Solutions to the Stokes Equations in a Polygon

Abstract

We present corner singularity expansion for the solutions of the Stokes equations in an arbitrary polygon under the stress boundary condition, with explicit expression of its singular part and quantitative estimate of its regular part. In particular, there is a countably infinite set of angles such that a corner with one of these angles would give the solution precisely one additional logarithmic singularity, whose explicit expression is found.