{"paper":{"title":"Singularity formation in the harmonic map flow with free boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Yannick Sire, Youquan Zheng","submitted_at":"2019-05-15T04:01:19Z","abstract_excerpt":"In the past years, there has been a new light shed on the harmonic map problem with free boundary in view of its connection with nonlocal equations. Here we fully exploit this link, considering the harmonic map flow with free boundary \\begin{equation}\\label{e:main0} \\begin{cases} u_t = \\Delta u\\text{ in }\\mathbb{R}^2_+\\times (0, T),\\\\ u(x,0,t) \\in \\mathbb{S}^1\\text{ for all }(x,0,t)\\in \\partial\\mathbb{R}^2_+\\times (0, T),\\\\ \\frac{du}{dy}(x,0,t)\\perp T_{u(x,0,t)}\\mathbb{S}^1\\text{ for all }(x,0,t)\\in \\partial\\mathbb{R}^2_+\\times (0, T),\\\\ u(\\cdot, 0) = u_0\\text{ in }\\mathbb{R}^2_+\n  \\end{cases}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05937","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}