{
  "abstract": "We prove global well-posedness of the periodic unidirectional Euler-alignment system in every dimension for supercritical dissipation of order $0<α<1$ and arbitrary non-vacuum initial data in the Sobolev class of the local theory. The key idea is to propagate simultaneously two moduli of continuity at critical scales for the density $ρ$ and the potential gradient $Γ=\\nablaΛ^{-α}u$, both of which have scaling-invariant amplitudes. We also establish exponential alignment of the velocity and exponential convergence of the density to a traveling profile.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25748",
  "author_total": 2,
  "authors": [
    {
      "name": "Changhui Tan"
    },
    {
      "name": "Liutang Xue"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8wkv1rxzs2tng.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25748",
  "fulltext_url": null,
  "id": "8wkv1rxzs2tng",
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  "landing_url": "https://arxiv.org/abs/2609.25748",
  "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": "W7214095476",
  "pdf_url": "https://arxiv.org/pdf/2609.25748",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8wkv1rxzs2tng.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25748",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25748"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global regularity for the unidirectional Euler-alignment system with supercritical dissipation",
  "title_text": "Global regularity for the unidirectional Euler-alignment system with supercritical dissipation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/8wkv1rxzs2tng",
  "venue": "arXiv",
  "versions": []
}