  In this note, which is of general stability theory interest, we discuss some
of the key assertions usually stated in the context of the transition to
turbulence problem. In particular, the two main points made here in the setting
of the transition problem are (i) the crucial dependence of the stability
results on whether the problem is considered on infinite or semi-infinite
domain, and (ii) the energy conservation by the nonlinear terms of the
Navier-Stokes equations. As an application, we demonstrate that the Couette
flow, when analyzed in the mathematical setting most correctly reflecting the
way the experiments are usually done, is spectrally unstable for finite
Reynolds numbers in apparent contradiction to the commonly accepted classical
century-old results. Also, the interrelation of various stability notions, the
effects of infinite dimensionality, the covariant nature of the transition
phenomena and how non-normality of the linear operators and finite-amplitude
instability fit into this picture are discussed as well.
