Numerical Solutions of Serrin’s Equations by Double Exponential Transformation

Abstract

We consider Serrin’s equations, which describe a steady flow of the incompressible viscous fluid caused by an interaction between a vortex filament and a planar wall. They are integro-differential equations with a singularity at an end point. By means of the double exponential transformation, we numerically solve their solutions with high accuracy, and compute a sufficient condition on the uniqueness of the solution.