Some existence result for a Stokes flow between two arbitrarily closed curves

Abstract

The problem of determining the slow viscous flow of a fluid between two arbitrarily closed curves is formulated as a system of Fredholm integral equations of the second kind, addying a pair of singularities located outside of the flow region. We show that the integral equations proposed here have a unique continuous solution, when the two closed curves are Lyapunov curves and the fluid velocity is continuous on these curves.