{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7QNDK7LSJORDUTXLYRO4VYEEXO","short_pith_number":"pith:7QNDK7LS","schema_version":"1.0","canonical_sha256":"fc1a357d724ba23a4eebc45dcae084bb9dfdbb94832fa719a6b01a7e3f8d4595","source":{"kind":"arxiv","id":"1105.2180","version":6},"attestation_state":"computed","paper":{"title":"On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chun Liu, Hao Wu, Xiang Xu","submitted_at":"2011-05-11T13:18:46Z","abstract_excerpt":"In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen-Leslie system through an appropriate energy variational approach under Parodi's relation, in which we can distinguish the conservative/dissipative parts of the induced elastic stress. Next, we prove global well-posedness and long-time behavior of the Ericksen-Leslie system under the assumption that the viscosity $\\mu_4$ is sufficiently large. Finally, under Parodi's"},"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":"1105.2180","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-11T13:18:46Z","cross_cats_sorted":[],"title_canon_sha256":"d602e8f3baffda24305dc6e088656dc90a7b110ab91f6780b70e3e8a7a9d8989","abstract_canon_sha256":"4916822ef4df366a67ec1a93b4aa3051604bc5cd074b41dbf87cf5a93a44f9f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:45.632631Z","signature_b64":"jN94bZfOAng+VOQjZ+KA8didh8lX8UD5sqmU5BoDrHeFy1OO95vqhlljZMn5PtULKcZYdBUWxojngKfbfB7vCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc1a357d724ba23a4eebc45dcae084bb9dfdbb94832fa719a6b01a7e3f8d4595","last_reissued_at":"2026-05-18T03:32:45.631839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:45.631839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chun Liu, Hao Wu, Xiang Xu","submitted_at":"2011-05-11T13:18:46Z","abstract_excerpt":"In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen-Leslie system through an appropriate energy variational approach under Parodi's relation, in which we can distinguish the conservative/dissipative parts of the induced elastic stress. Next, we prove global well-posedness and long-time behavior of the Ericksen-Leslie system under the assumption that the viscosity $\\mu_4$ is sufficiently large. Finally, under Parodi's"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2180","kind":"arxiv","version":6},"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":"1105.2180","created_at":"2026-05-18T03:32:45.631966+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.2180v6","created_at":"2026-05-18T03:32:45.631966+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2180","created_at":"2026-05-18T03:32:45.631966+00:00"},{"alias_kind":"pith_short_12","alias_value":"7QNDK7LSJORD","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7QNDK7LSJORDUTXL","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7QNDK7LS","created_at":"2026-05-18T12:26:22.705136+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/7QNDK7LSJORDUTXLYRO4VYEEXO","json":"https://pith.science/pith/7QNDK7LSJORDUTXLYRO4VYEEXO.json","graph_json":"https://pith.science/api/pith-number/7QNDK7LSJORDUTXLYRO4VYEEXO/graph.json","events_json":"https://pith.science/api/pith-number/7QNDK7LSJORDUTXLYRO4VYEEXO/events.json","paper":"https://pith.science/paper/7QNDK7LS"},"agent_actions":{"view_html":"https://pith.science/pith/7QNDK7LSJORDUTXLYRO4VYEEXO","download_json":"https://pith.science/pith/7QNDK7LSJORDUTXLYRO4VYEEXO.json","view_paper":"https://pith.science/paper/7QNDK7LS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.2180&json=true","fetch_graph":"https://pith.science/api/pith-number/7QNDK7LSJORDUTXLYRO4VYEEXO/graph.json","fetch_events":"https://pith.science/api/pith-number/7QNDK7LSJORDUTXLYRO4VYEEXO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7QNDK7LSJORDUTXLYRO4VYEEXO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7QNDK7LSJORDUTXLYRO4VYEEXO/action/storage_attestation","attest_author":"https://pith.science/pith/7QNDK7LSJORDUTXLYRO4VYEEXO/action/author_attestation","sign_citation":"https://pith.science/pith/7QNDK7LSJORDUTXLYRO4VYEEXO/action/citation_signature","submit_replication":"https://pith.science/pith/7QNDK7LSJORDUTXLYRO4VYEEXO/action/replication_record"}},"created_at":"2026-05-18T03:32:45.631966+00:00","updated_at":"2026-05-18T03:32:45.631966+00:00"}