{
  "abstract": "We consider the large time asymptotic behavior of solutions to the initial value problem for the incompressible Navier-Stokes equations in the whole space $\\mathbb{R}^d$ ($d\\ge 2$). When the initial velocity belongs to $L^1(\\mathbb{R}^d)$, it is well-known that its spatial integral vanishes as a consequence of the divergence-free compatibility condition. Taking this property into account, Carpio (1996) and Fujigaki-Miyakawa (2001) derived higher-order asymptotic formulas for the strong solutions. In this paper, we investigate the large time behavior of solutions when the initial velocity belongs to the Fourier-Herz space $\\widehat{L}^1(\\mathbb{R}^d)$, which provides a broader framework than $L^1(\\mathbb{R}^d)$ and imposes an additional condition in the low-frequency region. In particular, in the two-dimensional case, we show that an asymptotic profile different from those obtained by Carpio and Fujigaki-Miyakawa arises.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30902",
  "author_total": 2,
  "authors": [
    {
      "name": "Ikki Fukuda"
    },
    {
      "name": "Ryosuke Nakasato"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/am87sbe3wg1bt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30902",
  "fulltext_url": null,
  "id": "am87sbe3wg1bt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30902",
  "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": "W7214637080",
  "pdf_url": "https://arxiv.org/pdf/2609.30902",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/am87sbe3wg1bt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30902",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30902"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Asymptotic profiles for solutions to the incompressible Navier-Stokes equations in the critical Fourier-Herz spaces",
  "title_text": "Asymptotic profiles for solutions to the incompressible Navier-Stokes equations in the critical Fourier-Herz spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/am87sbe3wg1bt",
  "venue": "arXiv",
  "versions": []
}