{
  "abstract": "The Chern-Simons-Schrödinger equation (in the temporal gauge) arises as the Hamiltonian flow of the abelian Higgs energy on $\\mathbb R^2$. Manton (arXiv:hep-th/9701027) introduced the equation as a model for the dynamics of the critical points of the energy, known as vortices. He conjectured that, for a certain range of coupling constants, the vortex motion under the Chern-Simons-Schrödinger flow can be effectively captured by a first-order ODE on the moduli space of self-dual vortices constructed by Jaffe-Taubes (1980) and Samols (1992). As a first step towards a rigorous proof of Manton's conjecture, we formulate the Cauchy problem in DeTurck gauge within the natural energy space and prove global well-posedness. We also obtain, as a corollary of the well-posedness theory and the stability results in our previous work (arXiv:2603.24900), orbital stability of the self-dual vortices under the Chern-Simons-Schrödinger flow near self-dual coupling. The heart of our analysis lies in developing a geometric Littlewood-Paley theory based on the covariant heat equation in caloric gauge, which we use to perform a paradifferential-style decomposition of the Chern-Simons-Schrödinger equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13096",
  "author_total": 1,
  "authors": [
    {
      "name": "Jason Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fj2z251ch1bkx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13096",
  "fulltext_url": null,
  "id": "fj2z251ch1bkx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13096",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212478234",
  "pdf_url": "https://arxiv.org/pdf/2609.13096",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fj2z251ch1bkx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.13096",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13096"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Cauchy problem for Manton's Chern-Simons-Schrödinger equation",
  "title_text": "The Cauchy problem for Manton's Chern-Simons-Schrödinger equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/fj2z251ch1bkx",
  "venue": "arXiv",
  "versions": []
}