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

Irrotational Stokes flow in three system of coordinates