Landau Damping: Paraproducts and Gevrey Regularity

Jacob Bedrossian, Nader Masmoudi, Clément Mouhot

Research output: Contribution to journalArticlepeer-review


We give a new, simpler, but also and most importantly more general and robust, proof of nonlinear Landau damping on Td in Gevrey-1s regularity (s> 1 / 3) which matches the regularity requirement predicted by the formal analysis of Mouhot and Villani [67]. Our proof combines in a novel way ideas from the original proof of Landau damping Mouhot and Villani [67] and the proof of inviscid damping in 2D Euler Bedrossian and Masmoudi [10]. As in Bedrossian and Masmoudi [10], we use paraproduct decompositions and controlled regularity loss along time to replace the Newton iteration scheme of Mouhot and Villani [67]. We perform time-response estimates adapted from Mouhot and Villani [67] to control the plasma echoes and couple them to energy estimates on the distribution function in the style of the work Bedrossian and Masmoudi [10]. We believe the work is an important step forward in developing a systematic theory of phase mixing in infinite dimensional Hamiltonian systems.

Original languageEnglish (US)
Article number4
JournalAnnals of PDE
Issue number1
StatePublished - Jun 1 2016


  • Gevrey class
  • Landau damping
  • Nonlinear stability
  • Plasma physics
  • Vlasov equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Geometry and Topology
  • Mathematical Physics
  • General Physics and Astronomy


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