Nonlinear Landau damping for the unconfined Vlasov-Poisson system in 2D

@misc{ionescu2026nonlinear,
  title = {{Nonlinear Landau damping for the unconfined Vlasov-Poisson system in 2D}},
  author = {Alexandru D. Ionescu and Quoc-Hung Nguyen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28251},
  eprint = {2609.28251},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28251},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Nonlinear Landau damping for the unconfined Vlasov-Poisson system in 2D
AU  - Alexandru D. Ionescu
AU  - Quoc-Hung Nguyen
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28251
UR  - https://arxiv.org/abs/2609.28251
AB  - We prove nonlinear Landau damping for the two-dimensional Vlasov--Poisson system in the unconfined Euclidean setting near the homogeneous Poisson equilibrium μ(v)=1/2π(1+|v|^2)^−3/2. For small, smooth, localized, and neutral perturbations we establish global existence, quantitative pointwise decay estimates for the electric field, and scattering to free transport. The result we prove here appears to be the first nonlinear Landau damping result for solution of the unconfined 2D Vlasov--Poisson system. The uniform Penrose stability bound degenerates at low spatial frequencies, giving rise to weakly damped plasma oscillations. We separate a faster-decaying regular field from oscillatory components with temporal factors cos(t) and sin(t). The proof combines a Volterra representation of the density, weighted estimates for the characteristic flow and nonlinear moments, and integration by parts in time. Neutrality supplies the spatial cancellation needed in the critical two-dimensional estimates.
ER  -