Volume 3, Number 3, Summer 1995
A NECESSARY CONDITION FOR THE EXISTENCE OF
PLANE STOKES' FLOWS AROUND AN ELLIPSE
A. AVUDAINAYAGAM AND J. GEETHA
Abstract. Steady two-dimensional Stokes' flow in the
unbounded region exterior to an elliptic cylinder is considered.
The general solution for the stream function is derived in a
Joukowski coordinate system. It is shown that the governing
equations do not admit a solution for certain basic flows, and
a necessary condition for the existence of plane Stokes' flow
around an elliptic boundary is established. This condition
reduces to the earlier known condition  derived for the
circular cylinder. A few representative examples are shown.