{
  "abstract": "We consider the Cauchy problem for the nonlinear Dirac equation on a noncompact $N$-star metric graph $G$, \\[ \\mathrm{i}\\partial_t ψ= Dψ- |ψ|^{p-2}ψ, \\qquad ψ(0)=ψ_0, \\] where $p\\ge3$, $ψ:\\mathbb{R}\\times G\\to\\mathbb{C}^2$ and $D$ denotes the self-adjoint Dirac-Kirchhoff operator on $G$. Using Bourgain-type spaces defined through the spectral resolution of $D$, together with elementary $L^\\infty$ bounds for the Dirac flow and fractional Nemytskii estimates below the trace threshold, we prove local well-posedness for initial data \\[ ψ_0\\in H_D^s(G)\\cap L^\\infty(G;\\mathbb C^2), \\qquad 0\\le s<\\frac12 . \\] The corresponding solution belongs to \\[ C([0,T];H_D^s(G))\\cap X_T^{s,b}\\cap L^\\infty([0,T]\\times G). \\] Moreover, $\\|ψ(t)\\|_{L^2(G;\\mathbb{C}^2)}$ is conserved along the solution on the existence interval. We also establish a blow-up alternative in the combined $H_D^s$ and space-time $L^\\infty$ control norm.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Stud. Appl. Math. 157 (2026), no. 2: e70273",
  "arxiv": "2607.09303",
  "author_total": 2,
  "authors": [
    {
      "name": "Huichao Xing"
    },
    {
      "name": "Zhipeng Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/26gkas319v0dq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.09303",
  "fulltext_url": null,
  "id": "26gkas319v0dq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.09303",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.09303",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/26gkas319v0dq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2607.09303",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.09303"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Local well-posedness for nonlinear Dirac equation on $N$-star metric graphs",
  "title_text": "Local well-posedness for nonlinear Dirac equation on N-star metric graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/26gkas319v0dq",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1111/sapm.70273",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}