{
  "abstract": "Let $N^+$ and $N^-$ be disjoint compact smooth submanifolds of a Euclidean space, and let $Λ\\subset N^+\\times N^-$ be a compact smooth embedded submanifold prescribing admissible pairs of one-sided traces. Given a smooth family of separating hypersurfaces $Γ_t\\subset\\mathbb T^d$, we study harmonic map heat flows into $N^\\pm$ in the two moving phases, subject to \\[ (u^+,u^-)\\inΛ, \\qquad \\bigl(-\\partial_{ν_t}u^+,\\partial_{ν_t}u^-\\bigr) \\perp T_{(u^+,u^-)}Λ \\quad\\text{on }Γ_t. \\] For $q>d+2$, initial data in $W_q^{2-2/q}$ satisfying these conditions at $t=0$ generate a unique short-time strong solution in $W_q^{2,1}$, which is smooth up to the moving interface for every positive time; smooth initial data satisfying the compatibility conditions of every order yield solutions that are smooth up to the initial corner. We double the paired map across $Λ$ by normal reflection, which turns the interface conditions into a Dirichlet problem near the interface, and match this problem with the two bulk phases by an overlapping space-time Schwarz map inside a Schauder fixed-point argument. When the interface evolves independently by mean curvature, we also obtain a blow-up alternative in terms of its curvature and the two phase gradients. As an application, we prove local smooth solvability for the periodic matrix-valued sharp-interface system appearing in the convergence theory of Fei, Lin, Wang, and Zhang (\\emph{Invent. Math.} 233 (2023), 1--80).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07736",
  "author_total": 1,
  "authors": [
    {
      "name": "Xingyu Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/avk91102118kw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07736",
  "fulltext_url": null,
  "id": "avk91102118kw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07736",
  "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",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7220940285",
  "pdf_url": "https://arxiv.org/pdf/2610.07736",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/avk91102118kw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07736",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07736"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Short-time existence and uniqueness for two-phase harmonic map heat flow with a prescribed moving interface",
  "title_text": "Short-time existence and uniqueness for two-phase harmonic map heat flow with a prescribed moving interface",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/avk91102118kw",
  "venue": "arXiv",
  "versions": []
}