{"paper":{"title":"Refined blowup analysis and nonexistence of Type II blowups for an energy critical nonlinear heat equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Kelei Wang","submitted_at":"2021-01-18T17:43:51Z","abstract_excerpt":"We consider the energy critical semilinear heat equation $$ \\left\\{\\begin{aligned} &\\partial_t u-\\Delta u =|u|^{\\frac{4}{n-2}}u &\\mbox{in } {\\mathbb R}^n\\times(0,T),\\\\ &u(x,0)=u_0(x), \\end{aligned}\\right. $$ where $ n\\geq 3$, $u_0\\in L^\\infty({\\mathbb R}^n)$, and $T\\in {\\mathbb R}^+$ is the first blow up time. We prove that if $ n \\geq 7$ and $ u_0 \\geq 0$, then any blowup must be of Type I, i.e., \\[\\|u(\\cdot, t)\\|_{L^\\infty({\\mathbb R}^n)}\\leq C(T-t)^{-\\frac{1}{p-1}}.\\] A similar result holds for bounded convex domains. The proof relies on a reverse inner-outer gluing mechanism and delicate a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.07186","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2101.07186/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}