{
  "abstract": "We study finite-time condensation at zero frequency for the isotropic quasilinear 4-wave kinetic equation in three dimensions. With Schrodinger dispersion and a product interaction coefficient with exponent $β\\in(0,3/4]$, we construct global measure solutions $(g_t)_{t\\geq0}$ for every nonnegative initial measure $g_0$ with finite wave action and energy. We then establish the sharp threshold $β=1/4$ for finite-time condensation of the constructed solutions. For $β\\in[1/4,3/4]$, the constructed solutions satisfy $g_t(\\{0\\})=g_0(\\{0\\})$ for all $t\\geq0$. For $β\\in(0,1/4)$, every constructed solution with $(g_0)_{\\mathrm{ac}}\\neq0$ satisfies $\\|g_t-\\mathcal{N}_0δ_0\\|_{\\mathrm{TV}}\\leq C\\mathcal{N}_0(1+\\mathcal{N}_0^2t)^{-(1-4β)/40}$ for all $t\\geq0$, where $\\mathcal{N}_0=g_0([0,\\infty))$ and $C=C(β,g_0/\\mathcal{N}_0)>0$. In particular, for every $ζ\\in(0,1)$, there exists $T_ζ<\\infty$ such that $g_t(\\{0\\})\\geq(1-ζ)\\mathcal{N}_0$ for all $t\\geq T_ζ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25207",
  "author_total": 2,
  "authors": [
    {
      "name": "Siwei Luo"
    },
    {
      "name": "Jian-Guo Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31pazqxzdmt23.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25207",
  "fulltext_url": null,
  "id": "31pazqxzdmt23",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25207",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7223018139",
  "pdf_url": "https://arxiv.org/pdf/2610.25207",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31pazqxzdmt23.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.25207",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25207"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Condensation and Non-condensation in the Quasilinear 4-wave Kinetic Equation",
  "title_text": "Condensation and Non-condensation in the Quasilinear 4-wave Kinetic Equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/31pazqxzdmt23",
  "venue": "arXiv",
  "versions": []
}