{
  "abstract": "We study the incompressible Oldroyd-B system on $\\mathbb R^d$, $d\\ge2$, in the regime in which the velocity is the only dissipated quantity: the stress tensor undergoes neither relaxation nor diffusion. In this regime the operator $\\mathbb P\\operatorname{div}$ acting on symmetric stresses has an infinite-dimensional kernel consisting of exact stationary states, so no decay estimate can hold for the full stress tensor and the existing sharp-decay theory for dissipative systems does not apply. We identify the active pair $U=(u,Λ^{-1}\\mathbb P\\operatorname{div}τ)$ as the correct decaying observable and establish, in a critical hybrid Besov framework, a complete characterization of its large-time behavior. For $-d/2<σ_1<σ\\le d/2-1$ we prove that $\\|U(t)\\|_{\\mathcal H^σ}=O(t^{-(σ-σ_1)/2})$ holds if and only if the low-frequency part of $U_0$ belongs to $\\dot B^{σ_1}_{2,\\infty}$, and, for $σ<d/2-1$, that the two-sided estimate $\\|U(t)\\|_{\\mathcal H^σ}\\simeq t^{-(σ-σ_1)/2}$ holds if and only if the low-frequency part of $U_0$ belongs to a nondegenerate subclass $\\mathfrak B^{σ_1}_{2,\\infty}$ of $\\dot B^{σ_1}_{2,\\infty}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16228",
  "author_total": 4,
  "authors": [
    {
      "name": "Zhi Chen"
    },
    {
      "name": "Mingwen Fei"
    },
    {
      "name": "Lvqiao Liu"
    },
    {
      "name": "Jiahong Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fs0wx938v6cy1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16228",
  "fulltext_url": null,
  "id": "fs0wx938v6cy1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16228",
  "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": "W7221807839",
  "pdf_url": "https://arxiv.org/pdf/2610.16228",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fs0wx938v6cy1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16228",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16228"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp decay characterization for the Oldroyd-B system with only velocity dissipation",
  "title_text": "Sharp decay characterization for the Oldroyd-B system with only velocity dissipation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/fs0wx938v6cy1",
  "venue": "arXiv",
  "versions": []
}