Energy stability of plane Couette and Poiseuille flows: A conjecture

We will study the nonlinear stability of plane Couette and Poiseuille flows with Lyapunov second method by using classical L2-energy. prove that streamwise perturbations are L2-energy stable for any Reynolds number. This contradicts results Joseph (1966), Carmi (1969) Busse (1972), allows us to prove, a conjecture, critical numbers obtained along two-dimensional perturbations, spanwise as Orr (1907) had supposed. conclusion combined some recent Falsaperla et al. (2019) on respect tilted rolls, provides possible solution “mismatch” between values linear stability, monotonic energy experiments.