Abstract : In a torus and in any ergodic domain people in Plasma Physic introduce as an approximation an average of the particles over space and show in some case that the evolution of this space average can be described by a non linear parabolic equation for the velocity profile dubbed quasilinear approximation. In some case people relate it to the Landau Damping. Building on this observation I intend to review what can be said with genuine mathematic approaches about to this issue.