Non-axisymmetric flow of a viscoelastic fluid between rotating disks

It has been known for many years that two functions of the axial co-ordinate determine the axi-symmetric velocity field in the rotating disk problem in an incompressible Newtonian fluid. Recently, in the same configuration, the existence of a non-axisymmetric velocity field, determined by four functions of the axial co-ordinate, has been demonstrated. Because two functions of the axial co-ordinate determine the axi-symmetric velocity field in the above configuration for a class of viscoelastic fluids as well, it could be conjectured that four functions solve the non-axisymmetric problem for the same class of viscoelastic fluids. Here, this conjecture is shown to be true.