Landau damping

Of great interest in plasma physics is to determine whether excited charged particles in a non-equilibrium state will relax to neutrality or transition to a nontrivial coherent state. Due to the long range interaction between particles, the self-consistent generating electric field oscillates in time and disperses in space like a Klein-Gordon wave, known in the physical literature as plasma oscillations or Langmuir’s oscillatory waves. Landau in his original work addresses the decay of such an electric field, namely the energy exchange between the oscillatory electric field and charged particles, in a linearized setting. This talk will provide an overview of the recent mathematical advances in the nonlinear setting. The talk should be accessible to graduate students and the general audience.