{
  "abstract": "We study a two-parameter first-order hyperbolic relaxation approximation of the incompressible Navier--Stokes equations on the two-dimensional torus, under the derivative-level large-perturbation assumptions of Huang, Rohde and Zhang. Building on the auxiliary-system approach used in earlier pressure-convergence results, we introduce a non-autonomous linear corrector that carries the complete initial discrepancy, the linearized convection and the smooth consistency forcing. This corrector describes the full linear response; it is not asserted to be a purely acoustic component. An exact compensated energy identity, including a time integration by parts in the linearized convection term, yields an integrated gradient estimate for the velocity corrector. The two-dimensional Ladyzhenskaya inequality then bounds its quadratic self-interaction by $O(δ^2)$ in squared space-time $L^2$ norm. Consequently, the nonlinear remainder has weighted energy $O(δ^2)$, and its pressure and velocity components satisfy the $L^\\infty(0,T;L^2)$ bounds $C_Tδ/\\sqrtε$ and $C_Tδ$, respectively. In the sufficient parameter window $δ^2\\llε\\leqμ_*δ$, the pressure after subtraction of the linear corrector converges strongly to the incompressible pressure. A mean-zero Fourier-mode construction, transferred to the nonlinear system by the remainder estimate, shows that the uncorrected pressure need not converge even on time intervals bounded away from zero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13222",
  "author_total": 2,
  "authors": [
    {
      "name": "Leyang Wang"
    },
    {
      "name": "Wenlong Lin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5hjfhaa9q2t8n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13222",
  "fulltext_url": null,
  "id": "5hjfhaa9q2t8n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13222",
  "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": "W7213304147",
  "pdf_url": "https://arxiv.org/pdf/2609.13222",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5hjfhaa9q2t8n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2609.13222",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13222"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Linear Corrector Estimates and Corrected Pressure Convergence for a Two-Parameter Hyperbolic Relaxation of the Incompressible Navier--Stokes Equations",
  "title_text": "Linear Corrector Estimates and Corrected Pressure Convergence for a Two-Parameter Hyperbolic Relaxation of the Incompressible Navier--Stokes Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/5hjfhaa9q2t8n",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1515/tp-2026-0118",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}