On Landau damping

@article{Mouhot2009OnLD,
  title={On Landau damping},
  author={Cl{\'e}ment Mouhot and C{\'e}dric Villani},
  journal={Acta Mathematica},
  year={2009},
  volume={207},
  pages={29-201}
}
Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables, rather than exchanges of energy; phase mixing is the driving mechanism. The analysis involves new families of analytic norms, measuring regularity by comparison with solutions of the free transport equation… 

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