Large-Box Transition in Nonlinear Landau Damping for the Vlasov--Yukawa Equation
Abstract
We study nonlinear Landau damping for the Vlasov--Yukawa equation in the large-box regime, as a periodic box of length 2πL expands to the whole space. First, for d≥ 3, we prove global stability and scattering in an L-dependent Gevrey class, with estimates uniform for L≥ L0. The density obeys a two-regime upper bound: the whole-space decay rate ⟨ t⟩−d before the critical time scale Tdisp(L)∼ L, and a periodic phase-mixing bound in the rescaled time t/L thereafter. Second, to quantify the nonlinear resonance effect, we identify an echo-Volterra operator governing the nonlinear density memory, and provide sharp estimates for its non-collinear and collinear parts. The non-collinear time-frequency interactions remain uniformly bounded, whereas the collinear interactions do not become comparable to the background until the much later time scale Tcol(L)∼ Ld−1. Third, we investigate the stability and convergence of Sobolev initial data. For data of size ε, polynomial Sobolev smallness persists up to the time scale ε−1 Tcol(L). Within the shorter time scale Tdisp(L)∼ L, compatible periodic solutions converge locally, as L→∞, to a global solution of the whole-space Vlasov--Yukawa equation.
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BibTeX
@misc{he2026largebox,
title = {{Large-Box Transition in Nonlinear Landau Damping for the Vlasov--Yukawa Equation}},
author = {Ling-Bing He and Yue Luo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15238},
eprint = {2609.15238},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15238},
}
RIS
TY - UNPB
TI - Large-Box Transition in Nonlinear Landau Damping for the Vlasov--Yukawa Equation
AU - Ling-Bing He
AU - Yue Luo
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15238
UR - https://arxiv.org/abs/2609.15238
AB - We study nonlinear Landau damping for the Vlasov--Yukawa equation in the large-box regime, as a periodic box of length 2πL expands to the whole space. First, for d≥ 3, we prove global stability and scattering in an L-dependent Gevrey class, with estimates uniform for L≥ L_0. The density obeys a two-regime upper bound: the whole-space decay rate ⟨ t⟩^−d before the critical time scale T_disp(L)∼ L, and a periodic phase-mixing bound in the rescaled time t/L thereafter. Second, to quantify the nonlinear resonance effect, we identify an echo-Volterra operator governing the nonlinear density memory, and provide sharp estimates for its non-collinear and collinear parts. The non-collinear time-frequency interactions remain uniformly bounded, whereas the collinear interactions do not become comparable to the background until the much later time scale T_col(L)∼ L^d−1. Third, we investigate the stability and convergence of Sobolev initial data. For data of size ε, polynomial Sobolev smallness persists up to the time scale ε^−1 T_col(L). Within the shorter time scale T_disp(L)∼ L, compatible periodic solutions converge locally, as L→∞, to a global solution of the whole-space Vlasov--Yukawa equation.
ER -