Nonlinear Landau Damping for the Vlasov–Poisson System in R3: The Poisson Equilibrium

Alexandru D. Ionescu, Benoit Pausader, Xuecheng Wang, Klaus Widmayer

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We prove asymptotic stability of the Poisson homogeneous equilibrium among solutions of the Vlasov–Poisson system in the Euclidean space R3 . More precisely, we show that small, smooth, and localized perturbations of the Poisson equilibrium lead to global solutions of the Vlasov–Poisson system, which scatter to linear solutions at a polynomial rate as t→ ∞ . The Euclidean problem we consider here differs significantly from the classical work on Landau damping in the periodic setting, in several ways. Most importantly, the linearized problem cannot satisfy a “Penrose condition”. As a result, our system contains resonances (small divisors) and the electric field is a superposition of an electrostatic component and a larger oscillatory component, both with polynomially decaying rates.

Original languageEnglish (US)
Article number2
JournalAnnals of PDE
Issue number1
StatePublished - Jun 2024

All Science Journal Classification (ASJC) codes

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


  • Degenerate Penrose criterion
  • Landau damping
  • Nonlinear asymptotic stability
  • The Poisson equilibrium


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