A two dimensional slow viscous flow in semi-infinite parallel plates is investigated on the basis of the Stokes approximation.
This problem is formulated as a mixed boundary value problem. By using the function-theoretic method, we reduce it to a Fredholm integral equation of the second kind. From the solution of this integral equation and the condition on the flux of the flow, we obtain a formula by which we can determine an unknown real constant B introduced in the stream function. If B is found out, we can find two analytic functions. These analytic functions completely determine the stream function and the complex velocity of the flow.