{
  "abstract": "We provide a pathwise proof of global-in-time well-posedness for the generalised KPZ equation in the full subcritical regime by an adaptation of the strategy recently applied to the generalised Parabolic Anderson Model in [ES26]. Since this strategy relies crucially on the assumption that control of the supremum norm is sufficient to continue the solution, the main additional ingredient required is a treatment of the initial layer for gKPZ with merely $L^\\infty$ initial data, rather than the more usual setting of $C^θ$ initial data with $θ> 0$. Our approach is based on an expansion around a deterministic profile followed by the introduction of an integrating factor in order to remove the terms which have critical scaling at time $0$. For pedagogical purposes, we first demonstrate the proof techniques in the case of the standard $(1+1)$-dimensional KPZ equation before turning to the more computationally involved case of generalised KPZ.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09096",
  "author_total": 2,
  "authors": [
    {
      "name": "Jonas Sauer"
    },
    {
      "name": "Rhys Steele"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/829h1gsacfkbg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09096",
  "fulltext_url": null,
  "id": "829h1gsacfkbg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09096",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212031648",
  "pdf_url": "https://arxiv.org/pdf/2609.09096",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/829h1gsacfkbg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.09096",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09096"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Pathwise Global-in-Time Existence for the generalised KPZ Equation in the Full Subcritical Regime",
  "title_text": "Pathwise Global-in-Time Existence for the generalised KPZ Equation in the Full Subcritical Regime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/829h1gsacfkbg",
  "venue": "arXiv",
  "versions": []
}