{
  "abstract": "We prove the non-uniqueness of weak solutions to the three-dimensional hyper-viscous compressible Oldroyd-type model with general pressure laws and Newtonian viscous. Using an intermittent convex integration scheme, we construct non-unique weak solutions in $L_t^γW_x^{s,p}$ with $(s,p,γ)$ lies in the supercritical regime relative to the Ladyzhenskaya-Prodi-Serrin criteria. In addition, the Newtonian viscosity we considered contains the fractional viscosity $(-Δ)^α$, where the viscous exponent $α$ can be larger than the Lions exponent $5/4$. In the classical viscous case $α=1$, our construction also yields sharp non-uniqueness in $L_t^pL_x^\\infty$ for $1<p<2$. Furthermore, we obtain two singular-limit results. First, we prove the strong vanishing viscosity limit for any weak solutions in $H_{t,x}^{\\widetildeβ}$ to the compressible fundamental elastodynamic system. Second, $H_{t,x}^{\\widetildeβ}$ weak solutions to the incompressible Oldroyd-type model can be obtain as a low Mach number limit (incompressible limit) of a sequence of weak solutions to the compressible Oldroyd-type model. The main ingredient of our result is a new cancellation mechanism that overcomes the difficulty caused by the relative rigidity of the pressure. To the best of our knowledge, this is the first non-uniqueness results of weak solutions to the hyper-viscous compressible hydrodynamics equations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15073",
  "author_total": 4,
  "authors": [
    {
      "name": "Haobin Li"
    },
    {
      "name": "Peng Qu"
    },
    {
      "name": "Zirong Zeng"
    },
    {
      "name": "Mingxin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1je1hv36rb1nc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15073",
  "fulltext_url": null,
  "id": "1je1hv36rb1nc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15073",
  "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": "W7213292827",
  "pdf_url": "https://arxiv.org/pdf/2609.15073",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1je1hv36rb1nc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15073",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15073"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp non-uniqueness for the hyper-viscous compressible 3D Oldroyd-type models: Beyond the Lions exponent",
  "title_text": "Sharp non-uniqueness for the hyper-viscous compressible 3D Oldroyd-type models: Beyond the Lions exponent",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/1je1hv36rb1nc",
  "venue": "arXiv",
  "versions": []
}