{
  "abstract": "We are concerned with dissipation enhancement by divergence-free transport noise for stochastic \\(p(x)\\)-Laplace equations on \\(\\mathbb T^d\\), \\(d\\ge2\\). Spatially variable growth removes homogeneous scaling and produces two flux growth regimes. For periodic log-Hölder continuous exponents satisfying \\(2<p^-\\le p^+<\\infty\\), we first establish global variational well-posedness and the exact energy identity in the natural dual spaces. Under the additional condition \\(p^+<2d/(d-2)\\) when \\(d\\ge3\\), we then prove averaged algebraic decay with any prescribed coefficient, uniformly on bounded zero-mean \\(L^2\\) balls, by estimating the two flux powers separately. A deterministic lower bound yields strict averaged comparison with the unperturbed flow at prescribed positive times on shells with bounded gradient modular. We also prove optimality of the modular coercivity exponent \\(p^+\\) near zero. Finally, combining these estimates with intervalwise noise acceleration from the constant-exponent theory gives exponential decay in mean square and almost surely, with moments of the random prefactors bounded uniformly on the initial-data ball. For the exponential estimates, the noise depends on the prescribed rate and moment order; its intensity is fixed in time and its frequency range increases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21242",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiangwei Zhang"
    },
    {
      "name": "Juntao Wu"
    },
    {
      "name": "Shang Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8mvxkv555wgm5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21242",
  "fulltext_url": null,
  "id": "8mvxkv555wgm5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21242",
  "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.PR"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223992833",
  "pdf_url": "https://arxiv.org/pdf/2610.21242",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8mvxkv555wgm5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.21242",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21242"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Enhanced Dissipation by Transport Noise for Stochastic $p(x)$-Laplace Equations",
  "title_text": "Enhanced Dissipation by Transport Noise for Stochastic p(x)-Laplace Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/8mvxkv555wgm5",
  "venue": "arXiv",
  "versions": []
}