Georgia Institute of Technology College of Sciences

Landau damping is a collisionless stability result of considerable importance in plasma physics, as well as in galactic dynamics. Roughly speaking, it says that spatial waves are damped in time (very rapidly) by purely conservative mechanisms, on a time scale much lower than the effect of collisions. We shall present in this talk a recent work (joint with C. Villani) which provides the first positive mathematical result for this effect in the nonlinear regime, and qualitatively explains its robustness over extremely long time scales. Physical introduction and implications will also be discussed.