{
  "abstract": "We prove sharp well-posedness and soliton resolution for the half-wave maps equation on the real line $\\R$ in \\(H^{1/2}_\\bullet\\). This regularity threshold for global well-posedness is optimal, as we show by constructing examples of ill-posedness in \\(H^s_\\bullet\\) for any \\(s<1/2\\). Moreover, with the spectral assumption satisfied by a dense set of initial data in the energy space, we prove that solutions in \\(H^{1/2}_\\bullet\\) asymptotically decouple as an infinite superposition of solitons. Our results extend the known global well-posedness and finite soliton resolution for rational data in \\(H^\\infty_\\bullet\\) to sharp global well-posedness and soliton resolution for general data in \\(H^{1/2}_\\bullet\\). Different from rational solutions, general data can also involve an infinite discrete spectrum, which makes the reduction analysis framework on the finite rank no longer applicable. For sharp well-posedness, we present a new isometry criterion and stability results for resolvent transform in the explicit formula. For soliton resolution, we develop a spectral method for this equation based on direct resolvent analysis and a novel trace norm estimate that upgrades energy convergence to uniform convergence. Our argument also yields sharp well-posedness and soliton resolution for the generalized half-wave maps equation with targets in the complex Grassmannians, extending the classical sphere-valued case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36676",
  "author_total": 2,
  "authors": [
    {
      "name": "Fei Tang"
    },
    {
      "name": "Shou-Fu Tian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c3zqtnb0vt4cy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36676",
  "fulltext_url": null,
  "id": "c3zqtnb0vt4cy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36676",
  "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",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7224105072",
  "pdf_url": "https://arxiv.org/pdf/2610.36676",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c3zqtnb0vt4cy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36676",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36676"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp well-posedness and soliton resolution for the half-wave maps equation in $H^{1/2}_\\bullet$",
  "title_text": "Sharp well-posedness and soliton resolution for the half-wave maps equation in H^1/2_•",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/c3zqtnb0vt4cy",
  "venue": "arXiv",
  "versions": []
}