Near the corner, the flow can be assumed to be Stokes flow. Describing the two-dimensional planar problem by the cylindrical coordinates  with velocity components  defined by a stream function such that
the governing equation can be shown to be simply the biharmonic equation . The equation has to be solved with homogeneous boundary conditions (conditions taken for two walls separated by angle )
The Taylor scraping flow is similar to this problem but driven inhomogeneous boundary condition. The solution is obtained by the eigenfunction expansion,
where  are constants and the real part of the eigenvalues are always greater than unity. The eigenvalues  will be function of the angle , but regardless eigenfunctions can be written down for any ,
For antisymmetrical solution, the eigenfunction is even and hence  and the boundary conditions demand . The equations admits no real root when °. These complex eigenvalues indeed correspond to the moffatt eddies. The complex eigenvalue if given by  where
Here .