{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:E74ZXB2EAP7WPJCCCTBCQVCO6C","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5bfae524a3c461e7d16b71b99a9ad528f70a7f64dc60c3fa036d63aa0c28d1a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-24T12:51:37Z","title_canon_sha256":"56318d796ae428f54201b4b28258da264186532f24f774c84366c415c5a8e3ff"},"schema_version":"1.0","source":{"id":"1511.07685","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07685","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07685v1","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07685","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"E74ZXB2EAP7W","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"E74ZXB2EAP7WPJCC","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"E74ZXB2E","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:56356525adf020b58b7979e2a2ae86583fc09cdd0a950d5d82545c73ad45007e","target":"graph","created_at":"2026-05-18T01:26:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For any smoothly bounded domain $\\Omega\\subset\\mathbb R^n$, $n\\geq 3$, and any exponent $p>2^*=2n/(n-2)$ we study the Lane-Emden heat flow $u_t-\\Delta u = |u|^{p-2}u$ on $\\Omega\\times]0,\\infty[$ and establish local and global well-posedness results for the initial value problem with suitably small initial data $u\\big|_{t=0}=u_0$ in the Morrey space $L^{2,\\lambda}(\\Omega)$, where $\\lambda=4/(p-2)$. We contrast our results with results on instantaneous complete blow-up of the flow for certain large data in this space, similar to ill-posedness results of Galaktionov-Vazquez for the Lane-Emden flo","authors_text":"Michael Struwe, Simon Blatt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-24T12:51:37Z","title":"Well-posedness of the supercritical Lane-Emden heat flow in Morrey spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07685","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3e28d0b1d6760377aed674afa6baf3cfe0cb0af62983a300308028d594d79509","target":"record","created_at":"2026-05-18T01:26:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5bfae524a3c461e7d16b71b99a9ad528f70a7f64dc60c3fa036d63aa0c28d1a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-24T12:51:37Z","title_canon_sha256":"56318d796ae428f54201b4b28258da264186532f24f774c84366c415c5a8e3ff"},"schema_version":"1.0","source":{"id":"1511.07685","kind":"arxiv","version":1}},"canonical_sha256":"27f99b874403ff67a44214c228544ef080e921fd7b7a310d12f73f161ad43e6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27f99b874403ff67a44214c228544ef080e921fd7b7a310d12f73f161ad43e6c","first_computed_at":"2026-05-18T01:26:03.966443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:03.966443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U/dB6MJmyL+IgUoysAk8vHTT+lU2/JqSsAeKQX3Bt5zgWC/x4eAS3vYLsfQOwPfXRVQ93qK3K+uVixzWDu5UDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:03.967162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07685","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e28d0b1d6760377aed674afa6baf3cfe0cb0af62983a300308028d594d79509","sha256:56356525adf020b58b7979e2a2ae86583fc09cdd0a950d5d82545c73ad45007e"],"state_sha256":"cabf294ab05f7d4db96067c2c301a7c208a2de496bd02414b17c664b7ecd08da"}