{
  "abstract": "For $T>0$, we consider the Benjamin--Ono-type Dirac equation $$ i\\partial_tψ(x,t) + D(-Δ)^{\\frac{1}{2}}ψ(x,t) = D\\,G(ψ(x,t)), \\qquad (x,t)\\in\\mathbb{R}^n\\times[0,T], $$ where $(-Δ)^{\\frac{1}{2}}$ is the fractional Riesz operator, $D$ is the Dirac operator associated with the Clifford algebra of signature $(0,n)$, and $G(\\cdot)$ a scalar-valued quadratic nonlinearity. Under a pointwise anti-commutation condition on $ψ$ and a uniform dyadic regularity assumption on its spatial Fourier profile, we construct a unit-modulus gauge map $u$ by $ u=\\exp\\bigl(-iw\\bigr),$ where $w$ is a solution of $Dw=ψ$. Assuming, in addition, the stated regularity and commutation conditions on $w$, we show that the Plemelj components $u_{\\pm}=P_{\\pm}u$ solve a coupled Schrödinger system with gauge nonlinearities $P_{\\pm}N(ψ,u)$, where $$ N(ψ(x,t),u(x,t)) = -2P_{-}\\!\\left[ G(ψ(x,t)) \\right]u(x,t). $$ We also obtain a priori estimates for the homogeneous Sobolev seminorms $\\dot H^σ$ of $ψ(\\cdot,t)$, with at most exponential growth on $[0,T]$, together with estimates for $P_{\\pm}N(ψ(\\cdot,t),u(\\cdot,t))$. Combining these bounds with the homogeneous and inhomogeneous Strichartz estimates for the Schrödinger system, we obtain, for $n\\geq 3$ and every sharp Schrödinger admissible pair $(q,p)$, an a priori Strichartz-type estimate for $ψ$ in $L_T^q\\dot W_x^{σ,p}$, expressed in terms of the initial datum $ψ(\\cdot,0)$ and the a priori controls of $ψ$ in $L_T^\\infty H_x^{σ+1}$ and $L_T^\\infty L_x^\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16842",
  "author_total": 1,
  "authors": [
    {
      "name": "Nelson Faustino"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ev0qx57sxff7x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16842",
  "fulltext_url": null,
  "id": "ev0qx57sxff7x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16842",
  "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"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7221764347",
  "pdf_url": "https://arxiv.org/pdf/2610.16842",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ev0qx57sxff7x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:16Z",
      "native_id": "2610.16842",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16842"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Gauge Transforms and Strichartz Estimates for Benjamin--Ono-Type Dirac Equations",
  "title_text": "Gauge Transforms and Strichartz Estimates for Benjamin--Ono-Type Dirac Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:16Z",
  "url": "https://research.draconitic.com/paper/ev0qx57sxff7x",
  "venue": "arXiv",
  "versions": []
}