{
  "abstract": "We study the Cauchy problem for the energy-critical Schrödinger map into the 2-sphere: \\[ \\partial_{t}u = u\\timesΔu, \\quad (t,x)\\in\\mathbb{R}^{1+2}, \\quad u(t,x)\\in\\mathbb{S}^2 \\] for equivariant initial data of homotopy degree $k=1$. Given any integer $L\\in\\mathbb{N}_+$, we exhibit a set of initial data arbitrarily close to the ground state harmonic map in the energy norm such that the corresponding solution blows up in finite time with a quantized rate \\[ λ(t)\\sim \\frac{\\left(T-t\\right)^L}{\\left|\\log(T-t)\\right|^{\\frac{2L}{2L-1}}} \\quad\\mbox{as}\\ \\ t\\uparrow T. \\] Our proof is inspired by the techniques developed for the energy-critical harmonic map heat flow in a similar context by Raphaël and Schweyer [Anal. PDE 7 (2014), 1713--1805]. However, its adaptation to a Schrödinger-type equation requires the introduction of a new energy-Virial-Morawetz Lyapunov functional tailored to quantized slow blowup dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20313",
  "author_total": 4,
  "authors": [
    {
      "name": "Jacek Jendrej"
    },
    {
      "name": "Jitao Xu"
    },
    {
      "name": "Xu Yuan"
    },
    {
      "name": "Lifeng Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3w6y1kc0a914x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20313",
  "fulltext_url": null,
  "id": "3w6y1kc0a914x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20313",
  "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": "W7221953072",
  "pdf_url": "https://arxiv.org/pdf/2610.20313",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3w6y1kc0a914x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.20313",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20313"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Quantized slow blowup dynamics for the energy-critical Schrödinger map flow",
  "title_text": "Quantized slow blowup dynamics for the energy-critical Schrödinger map flow",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/3w6y1kc0a914x",
  "venue": "arXiv",
  "versions": []
}