Geometric Singularities of the Stokes Problem

Abstract

When the domain is a polygon of ${ℝ}^{\mathrm{2}}$, the solution of a partial differential equation is written as a sum of a regular part and a linear combination of singular functions. The purpose of this paper is to present explicitly the singular functions of Stokes problem. We prove the Kondratiev method in the case of the crack. We finish by giving some regularity results.