{"paper":{"title":"Infinite time blow-up and slow decay for the six dimensional energy-critical heat equation with self-similarly decaying initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The six-dimensional energy-critical heat equation with self-similar initial decay admits sign-changing solutions that blow up only after infinite time and nonnegative solutions whose decay is strictly slower than self-similar.","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erbol Zhanpeisov, Jin Takahashi, Kotaro Hisa","submitted_at":"2026-04-22T09:59:14Z","abstract_excerpt":"We consider the six dimensional energy-critical semilinear heat equation with self-similarly decaying initial data. Our main result shows the existence of sign-changing solutions that exhibit infinite-time blow-up and nonnegative solutions that decay strictly more slowly than the self-similar rate. Moreover, the blow-up and decay rates are not uniquely determined by the decay rate of the initial data, but exhibit a certain flexibility depending on the construction. The proof is based on gluing suitably rescaled bubbles to forward self-similar solutions."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our main result shows the existence of sign-changing solutions that exhibit infinite-time blow-up and nonnegative solutions that decay strictly more slowly than the self-similar rate. Moreover, the blow-up and decay rates are not uniquely determined by the decay rate of the initial data, but exhibit a certain flexibility depending on the construction.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The gluing of suitably rescaled bubbles to forward self-similar solutions can be carried out rigorously for initial data with the given self-similar decay, without destroying the desired long-time behavior.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Existence of infinite-time blow-up sign-changing solutions and slower-than-self-similar decaying nonnegative solutions for the 6D energy-critical heat equation with self-similarly decaying initial data.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The six-dimensional energy-critical heat equation with self-similar initial decay admits sign-changing solutions that blow up only after infinite time and nonnegative solutions whose decay is strictly slower than self-similar.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3794b65d2b2839faf573e5e9947304ef74f45acefc3372534d995b2831fc1b98"},"source":{"id":"2604.20396","kind":"arxiv","version":2},"verdict":{"id":"8b721734-c458-4097-9521-51b8ee0b8fd7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T23:52:39.854490Z","strongest_claim":"Our main result shows the existence of sign-changing solutions that exhibit infinite-time blow-up and nonnegative solutions that decay strictly more slowly than the self-similar rate. Moreover, the blow-up and decay rates are not uniquely determined by the decay rate of the initial data, but exhibit a certain flexibility depending on the construction.","one_line_summary":"Existence of infinite-time blow-up sign-changing solutions and slower-than-self-similar decaying nonnegative solutions for the 6D energy-critical heat equation with self-similarly decaying initial data.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The gluing of suitably rescaled bubbles to forward self-similar solutions can be carried out rigorously for initial data with the given self-similar decay, without destroying the desired long-time behavior.","pith_extraction_headline":"The six-dimensional energy-critical heat equation with self-similar initial decay admits sign-changing solutions that blow up only after infinite time and nonnegative solutions whose decay is strictly slower than self-similar."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.20396/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T14:42:24.404792Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-20T02:00:17.019128Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6cfbcdc98ebdeac095dfa6ce7cd095161fe469771faad6276fef250602b653c0"},"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"}