  The problem of two-dimensional steady nonlinear dynamics in plane Couette
flow is revisited using homotopy from either plane Poiseuille flow or from
plane Couette flow perturbed by a small symmetry-preserving identity operator.
Our results show that it is not possible to obtain the nonlinear plane Couette
flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids,
14, 667 (1995)] using their Poiseuille-Couette homotopy. We also demonstrate
that the steady solutions obtained by Mehta and Healey [Phys. Fluids, 17, 4108
(2005)] for small symmetry-preserving perturbations are influenced by an
artefact of the modified system of equations used in their paper. However,
using a modified version of their model does not help to find plane Couette
flow solution in the limit of vanishing symmetry-preserving perturbations
either. The issue of the existence of two-dimensional nonlinear steady states
in plane Couette flow remains unsettled.
