{
  "abstract": "We study the three-dimensional incompressible Navier--Stokes equations with a componentwise nonlinear damping term of the form $α\\sum_{k=1}^3 u_k^{2m+1}e_k$ in Fourier and Fourier-- Gevrey spaces based on $\\mathcal{X}^0(\\mathbb{R}^3)$. We first establish local-in-time existence and uniqueness of solutions and obtain the corresponding unique maximal solutions. We then derive blow-up criteria in the Fourier--Gevrey framework, including an integral blow-up criterion in a weaker exponential weight. Moreover, we establish a quantitative lower bound for the solution near a possible finite maximal existence time. By iterating the loss of exponential weight, we finally obtain a corresponding lower bound in the unweighted Fourier space $\\mathcal{X}^0(\\mathbb{R}^3)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32719",
  "author_total": 2,
  "authors": [
    {
      "name": "Jamel Benameur"
    },
    {
      "name": "Lotfi Jlali"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2mqfxtf56c8ay.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32719",
  "fulltext_url": null,
  "id": "2mqfxtf56c8ay",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32719",
  "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": "W7214736998",
  "pdf_url": "https://arxiv.org/pdf/2609.32719",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2mqfxtf56c8ay.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32719",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32719"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Blow-Up of Modified Navier--Stokes Equations in Nonhomogeneous Fourier Spaces",
  "title_text": "Blow-Up of Modified Navier--Stokes Equations in Nonhomogeneous Fourier Spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/2mqfxtf56c8ay",
  "venue": "arXiv",
  "versions": []
}