TL;DR
This paper discusses nonlinear Landau damping in the Vlasov-Poisson system, exploring analyticity frameworks, plasma confinement scenarios, and establishing damping results for Vlasov-Riesz systems including the Vlasov-Dirac-Benney system.
Contribution
It introduces new results on nonlinear Landau damping for Vlasov-Riesz systems, including the borderline Vlasov-Dirac-Benney system, within sharp analytic spaces.
Findings
Nonlinear Landau damping established for Vlasov-Riesz systems.
Analytic framework extends to plasmas on torus and in space.
Includes the borderline Vlasov-Dirac-Benney system.
Abstract
We provide few remarks on nonlinear Landau damping that concerns decay of the electric field in the classical Vlasov-Poisson system near spatially homogenous equilibria. In particular, this includes the analyticity framework, \`a la Grenier-Nguyen-Rodnianski, for non specialists, treating the analytic case studied by Mouhot-Villani, among other remarks for plasmas confined on a torus and in the whole space. Finally, we also establish the nonlinear Landau damping for a family of Vlasov-Riesz systems, which are new and surprisingly include the borderline Vlasov-Dirac-Benney system in the sharp analytic spaces.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Control and Stability of Dynamical Systems · Nonlinear Dynamics and Pattern Formation