Periodic Fundamental Solution of the Two-Dimensional Stokes Equations

Abstract

A doubly periodic fundamental solution of the Stokes equations is constructed on the basis of the author’s fundamental solution of a Poisson equation recently published in this Journal. It is represented by the Weierstrass elliptic function in the complex plane. As an example of its application, a generalized Darcy law for a lattice of thin circular cylinders is derived using the general solution extended from the fundamental solution.