{"paper":{"title":"On the stability of type II blowup for the 1-corotational energy supercritical harmonic heat flow","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Slim Ibrahim, Tej-Eddine Ghoul, Van Tien Nguyen","submitted_at":"2016-11-27T17:30:38Z","abstract_excerpt":"We consider the energy supercritical harmonic heat flow from $\\mathbb{R}^d$ into the $d$-sphere $\\mathbb{S}^d$ with $d \\geq 7$. Under an additional assumption of 1-corotational symmetry, the problem reduces to the one dimensional semilinear heat equation $$\\partial_t u = \\partial^2_r u + \\frac{(d-1)}{r}\\partial_r u - \\frac{(d-1)}{2r^2}\\sin(2u).$$ We construct for this equation a family of $\\mathcal{C}^{\\infty}$ solutions which blow up in finite time via concentration of the universal profile $$u(r,t) \\sim Q\\left(\\frac{r}{\\lambda(t)}\\right),$$ where $Q$ is the stationary solution of the equatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08877","kind":"arxiv","version":3},"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"}