{
  "abstract": "We study the equivariant Chern--Simons gauged Landau--Lifshitz equation in $\\mathbb R^2$. For equivariance index $m\\ge2$ and a potential $V\\in C^{3,1}([0,2])$ satisfying $V(0)=V'(0)=0$, we first establish local well-posedness for the Cauchy problem at the $H^2$ level, with the sphere constraint written in the natural affine space $u-\\vec n\\in H^2$. For nonnegative $V$ we then consider an $m$--equivariant ground state of $H_ω=E+ωM$, $ω>0$. Under a constrained nondegeneracy condition for the polar Hessian, the conserved energy and mass give orbital stability in $H^1$. A Gustafson--Shatah type continuation argument, in which the Chern--Simons feedback is treated as a tame nonlocal zeroth-order perturbation, upgrades this conditional stability to global $H^2$ existence for all $H^2$ initial data sufficiently close to the ground state orbit in $H^1$. For the quadratic potential we also verify the nondegeneracy condition in a nonempty interior near-BPS regime approaching the self-dual point $(κ,ω)=(1,0)$. This yields a concrete family of globally defined orbitally stable ground states.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01596",
  "author_total": 3,
  "authors": [
    {
      "name": "Guanghui Jin"
    },
    {
      "name": "Jinmyoung Seok"
    },
    {
      "name": "Jianjun Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0hwhrjnwr8d4b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01596",
  "fulltext_url": null,
  "id": "0hwhrjnwr8d4b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01596",
  "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/2611.01596",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0hwhrjnwr8d4b.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01596",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01596"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Orbital stability for the equivariant Chern--Simons gauged Landau--Lifshitz equation in $\\mathbb{R}^2$",
  "title_text": "Orbital stability for the equivariant Chern--Simons gauged Landau--Lifshitz equation in ℝ^2",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/0hwhrjnwr8d4b",
  "venue": "arXiv",
  "versions": []
}