  In this work a result of existence and uniqueness for a plane cavity driven
steady flow is deduced using an analytical method for the resolution of a
linear partial differential problem on a triangular domain. The solution admits
a symbolic expression based on integration over the domain. Some examples of
flow are computed and graphed. In particular, it is shown a realistic example
of a shear-forced flow with two eddies, usually computed only by numerical
methods. The mathematical techniques used for the demonstration of the main
result are elementary.
