{
  "abstract": "We establish intrinsic continuation criteria and finite-energy global solvability for the stochastic tamed Navier--Stokes equations on $\\mathbb R^3$ driven simultaneously by multiplicative cylindrical Wiener and compensated Poisson noise. Under local coefficient hypotheses, the maximal local $L^p$ solution, $p>3$, satisfies a blow-up alternative independent of auxiliary cutoffs and a Serrin criterion with time exponent $2p/(p-3)$. Additional coercivity of the taming term and compatible $L^2$ and gradient noise bounds yield the global well-posedness theory for divergence-free initial data $u_0\\in L^p(Ω;L^p)\\cap L^2(Ω;L^2)$. No smallness or initial $H^1$ regularity is required. The solution has càdlàg $L^p\\cap L^2$ paths and gains $H^1$ regularity at positive times, with time-weighted $H^1$ and $H^2$ estimates. The proof combines finite-energy persistence with endpoint completion that retains terminal Poisson jumps and permits restart in the original uniqueness class.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29411",
  "author_total": 2,
  "authors": [
    {
      "name": "Bikram Podder"
    },
    {
      "name": "Surendra Kumar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4stkvrqz08b42.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29411",
  "fulltext_url": null,
  "id": "4stkvrqz08b42",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29411",
  "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|Navier-Stokes equation solutions"
    ]
  ],
  "openalex": "W7214299698",
  "pdf_url": "https://arxiv.org/pdf/2609.29411",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4stkvrqz08b42.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29411",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29411"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Stochastic Tamed Navier--Stokes Equations with Wiener and Jump Noise on $\\mathbb R^3$. II. Global $L^p$ Well-Posedness",
  "title_text": "Stochastic Tamed Navier--Stokes Equations with Wiener and Jump Noise on ℝ^3. II. Global L^p Well-Posedness",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/4stkvrqz08b42",
  "venue": "arXiv",
  "versions": []
}