{
  "abstract": "In this paper, we study the endpoint regularity of weak solutions to the inhomogeneous Rivière system $$ -Δu=Ω\\cdot\\nabla u+f \\qquad\\text{in }B_1\\subset\\mathbb R^2, $$ with an antisymmetric potential $Ω\\in L^2$ and a local Hardy drift term $f\\in h^1$. We construct a continuous solution in $W_0^{1,2}$, which fails to belong to $W^{2,1}$ in every neighborhood of the origin, even when $\\|Ω\\|_{L^2}$ is arbitrarily small. Smooth truncations further show that the corresponding uniform interior $W^{2,1}$ estimate fails even for smooth solutions and coefficients. Thus, the $L\\log L$ assumption ensuring local $W^{2,1}$ regularity cannot in general be replaced by componentwise local Hardy data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01877",
  "author_total": 3,
  "authors": [
    {
      "name": "Yu-Ting Kang"
    },
    {
      "name": "Wen-Juan Qi"
    },
    {
      "name": "Zhao-Min Sun"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/442x4r3weaejp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01877",
  "fulltext_url": null,
  "id": "442x4r3weaejp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01877",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01877",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/442x4r3weaejp.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01877",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01877"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On $W^{2,1}$-Regularity for Rivière's System with a Local Hardy Drift",
  "title_text": "On W^2,1-Regularity for Rivière's System with a Local Hardy Drift",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/442x4r3weaejp",
  "venue": "arXiv",
  "versions": []
}