  Irrotational flow is described with the second order elliptic partial
differential equation $E^2\psi=0,$ where $\psi$ is the function to be derived
and $E^2$ is the Stokes operator. In the present paper we derive the solution
of $E^2\psi=0$ in three axisymmetric system of coordinates: the parabolic, the
tangent sphere and the cardioid. We prove that Stokes equation separates
variables in the parabolic coordinate system, but it R-separates variables in
the other two. At the end of this manuscript we summarize all the known results
for the 0-eigenspace of $E^2$ in axisymmetric system of coordinates.
