{"paper":{"title":"Type II blow-up mechanism for supercritical harmonic map heat flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pawe{\\l} Biernat, Yukihiro Seki","submitted_at":"2016-01-08T11:09:19Z","abstract_excerpt":"The harmonic map heat flow is a geometric flow well known to produce solutions whose gradient blows up in finite time. A popular model for investigating the blow-up is the heat flow for maps $\\mathbb R^{d}\\to S^{d}$, restricted to equivariant maps. This model displays a variety of possible blow-up mechanisms, examples include self-similar solutions for $3\\le d\\le 6$ and a so-called Type II blow-up in the critical dimension $d=2$. Here we present the first constructive example of Type II blow-up in higher dimensions: for each $d\\ge7$ we construct a countable family of Type II solutions, each ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01831","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"}