{"paper":{"title":"Infinite time blow-up for half-harmonic map flow from $\\mathbb{R}$ into $\\mathbb{S}^1$","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":"2017-11-15T02:52:26Z","abstract_excerpt":"We study infinite time blow-up phenomenon for the half-harmonic map flow \\begin{equation}\\label{e:main00} \\left\\{\\begin{array}{ll}\n  u_t = -(-\\Delta)^{\\frac{1}{2}}u + \\left(\\frac{1}{2\\pi}\\int_{\\mathbb{R}}\\frac{|u(x)-u(s)|^2}{|x-s|^2}ds\\right)u\\quad\\text{ in }\\mathbb{R}\\times (0, \\infty),\n  u(\\cdot, 0) = u_0\\quad\\text{ in }\\mathbb{R},\n  \\end{array} \\right. \\end{equation} with a function $u:\\mathbb{R}\\times [0, \\infty)\\to \\mathbb{S}^1$. Let $q_1,\\cdots, q_k$ be distinct points in $\\mathbb{R}$, there exist an initial datum $u_0$ and smooth functions $\\xi_j(t)\\to q_j$, $0<\\mu_j(t)\\to 0$, as $t\\to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05387","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"}