{
  "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 $d\\ge 3$, we prove global stability and scattering in an $L$-dependent Gevrey class, with estimates uniform for $L\\ge L_0$. The density obeys a two-regime upper bound: the whole-space decay rate $\\langle t\\rangle^{-d}$ before the critical time scale $T_{\\rm disp}(L)\\sim L$, 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 $T_{\\rm col}(L)\\sim L^{d-1}$. Third, we investigate the stability and convergence of Sobolev initial data. For data of size $\\varepsilon$, polynomial Sobolev smallness persists up to the time scale $\\varepsilon^{-1} T_{\\rm col}(L)$. Within the shorter time scale $T_{\\rm disp}(L)\\sim L$, compatible periodic solutions converge locally, as $L\\to\\infty$, to a global solution of the whole-space Vlasov--Yukawa equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15238",
  "author_total": 2,
  "authors": [
    {
      "name": "Ling-Bing He"
    },
    {
      "name": "Yue Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4gf1frznhvvgr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15238",
  "fulltext_url": null,
  "id": "4gf1frznhvvgr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15238",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7213301085",
  "pdf_url": "https://arxiv.org/pdf/2609.15238",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4gf1frznhvvgr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15238",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15238"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Large-Box Transition in Nonlinear Landau Damping for the Vlasov--Yukawa Equation",
  "title_text": "Large-Box Transition in Nonlinear Landau Damping for the Vlasov--Yukawa Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/4gf1frznhvvgr",
  "venue": "arXiv",
  "versions": []
}