{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:6MGTL4RZOJRJ7G5LQJGTCTDQSW","short_pith_number":"pith:6MGTL4RZ","schema_version":"1.0","canonical_sha256":"f30d35f23972629f9bab824d314c7095badf84030d0ae610c700632cfa0bbd4e","source":{"kind":"arxiv","id":"1205.1269","version":3},"attestation_state":"computed","paper":{"title":"Remarks of Global Wellposedness of Liquid Crystal Flows and Heat Flows of Harmonic Maps in Two Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dong Li, Xiaoyi Zhang, Zhen Lei","submitted_at":"2012-05-07T02:32:20Z","abstract_excerpt":"We consider the Cauchy problem to the two-dimensional incompressible liquid crystal equation and the heat flows of harmonic maps equation. Under a natural geometric angle condition, we give a new proof of the global well-posedness of smooth solutions for a class of large initial data in energy space. This result was originally obtained by Ding-Lin in \\cite{DingLin} and Lin-Lin-Wang in \\cite{LinLinWang}. Our main technical tool is a rigidity theorem which gives the coercivity of the harmonic energy under certain angle condition. Our proof is based on a frequency localization argument combined w"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1205.1269","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-05-07T02:32:20Z","cross_cats_sorted":[],"title_canon_sha256":"aa6cf3491ee267cc161a4a2fba71864fc2b01e7bb333ebc88aa0fac4945b92dc","abstract_canon_sha256":"10fddac162f326de33061884979c717165c10ee10c33c5106dfa3a1eb21124ff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:02.404439Z","signature_b64":"5OmJKj0DHpJ7PMcr/i8XWF4ZbJ8STrc4b1RVwVvpZbxHDM+BXIMKBj588ufLJD7DKqxUruCKIcZkYYEFSCewBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f30d35f23972629f9bab824d314c7095badf84030d0ae610c700632cfa0bbd4e","last_reissued_at":"2026-05-18T03:44:02.403881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:02.403881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Remarks of Global Wellposedness of Liquid Crystal Flows and Heat Flows of Harmonic Maps in Two Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dong Li, Xiaoyi Zhang, Zhen Lei","submitted_at":"2012-05-07T02:32:20Z","abstract_excerpt":"We consider the Cauchy problem to the two-dimensional incompressible liquid crystal equation and the heat flows of harmonic maps equation. Under a natural geometric angle condition, we give a new proof of the global well-posedness of smooth solutions for a class of large initial data in energy space. This result was originally obtained by Ding-Lin in \\cite{DingLin} and Lin-Lin-Wang in \\cite{LinLinWang}. Our main technical tool is a rigidity theorem which gives the coercivity of the harmonic energy under certain angle condition. Our proof is based on a frequency localization argument combined w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1269","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1205.1269","created_at":"2026-05-18T03:44:02.403965+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.1269v3","created_at":"2026-05-18T03:44:02.403965+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1269","created_at":"2026-05-18T03:44:02.403965+00:00"},{"alias_kind":"pith_short_12","alias_value":"6MGTL4RZOJRJ","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_16","alias_value":"6MGTL4RZOJRJ7G5L","created_at":"2026-05-18T12:26:56.085431+00:00"},{"alias_kind":"pith_short_8","alias_value":"6MGTL4RZ","created_at":"2026-05-18T12:26:56.085431+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6MGTL4RZOJRJ7G5LQJGTCTDQSW","json":"https://pith.science/pith/6MGTL4RZOJRJ7G5LQJGTCTDQSW.json","graph_json":"https://pith.science/api/pith-number/6MGTL4RZOJRJ7G5LQJGTCTDQSW/graph.json","events_json":"https://pith.science/api/pith-number/6MGTL4RZOJRJ7G5LQJGTCTDQSW/events.json","paper":"https://pith.science/paper/6MGTL4RZ"},"agent_actions":{"view_html":"https://pith.science/pith/6MGTL4RZOJRJ7G5LQJGTCTDQSW","download_json":"https://pith.science/pith/6MGTL4RZOJRJ7G5LQJGTCTDQSW.json","view_paper":"https://pith.science/paper/6MGTL4RZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.1269&json=true","fetch_graph":"https://pith.science/api/pith-number/6MGTL4RZOJRJ7G5LQJGTCTDQSW/graph.json","fetch_events":"https://pith.science/api/pith-number/6MGTL4RZOJRJ7G5LQJGTCTDQSW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6MGTL4RZOJRJ7G5LQJGTCTDQSW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6MGTL4RZOJRJ7G5LQJGTCTDQSW/action/storage_attestation","attest_author":"https://pith.science/pith/6MGTL4RZOJRJ7G5LQJGTCTDQSW/action/author_attestation","sign_citation":"https://pith.science/pith/6MGTL4RZOJRJ7G5LQJGTCTDQSW/action/citation_signature","submit_replication":"https://pith.science/pith/6MGTL4RZOJRJ7G5LQJGTCTDQSW/action/replication_record"}},"created_at":"2026-05-18T03:44:02.403965+00:00","updated_at":"2026-05-18T03:44:02.403965+00:00"}