Asymptotic Stability of Equilibria for Screened Vlasov–Poisson Systems via Pointwise Dispersive Estimates

Daniel Han-Kwan, Toan T. Nguyen, Frédéric Rousset

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1 Scopus citations

Abstract

We revisit the proof of Landau damping near stable homogenous equilibria of Vlasov–Poisson systems with screened interactions in the whole space Rd (for d≥ 3) that was first established by Bedrossian, Masmoudi and Mouhot in [5]. Our proof follows a Lagrangian approach and relies on precise pointwise in time dispersive estimates in the physical space for the linearized problem that should be of independent interest. This allows to cut down the smoothness of the initial data required in [5] (roughly, we only need Lipschitz regularity). Moreover, the time decay estimates we prove are essentially sharp, being the same as those for free transport, up to a logarithmic correction.

Original languageEnglish (US)
Article number18
JournalAnnals of PDE
Volume7
Issue number2
DOIs
StatePublished - Dec 2021

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics
  • Geometry and Topology
  • Mathematical Physics
  • Physics and Astronomy(all)

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