  Critical Reynolds numbers for the monotone exponential energy stability of
Couette and Poiseuille plane flows were obtained by Orr 1907 \cite{Orr1907} in
a famous paper, and by Joseph 1966 \cite{Joseph1966}, Joseph and Carmi 1969
\cite{JosephCarmi1969} and Busse 1972 \cite{Busse1972}. All these authors
obtained their results applying variational methods to compute the maximum of a
functional ratio derived from the Reynolds-Orr energy identity. Orr and Joseph
obtained different results, for instance in the Couette case Orr computed the
critical Reynolds value of 44.3 (on spanwise perturbations) and Joseph 20.65
(on streamwise perturbations).
  Recently in Falsaperla et al. 2022 \cite{FalsaperlaMulonePerrone2022}, the
authors conjectured that the search of the maximum should be restricted to a
subspace of the space of kinematically admissible perturbations. With this
conjecture, the critical nonlinear energy Reynolds number was found among
spanwise perturbations (a Squire theorem for nonlinear systems).
  With a direct proof and an appropriate and original decomposition of the
dissipation terms in the Reynolds-Orr identity we show the validity of this
conjecture in the space of three dimensional perturbations.
