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 (...