{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7QNDK7LSJORDUTXLYRO4VYEEXO","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":"4916822ef4df366a67ec1a93b4aa3051604bc5cd074b41dbf87cf5a93a44f9f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-11T13:18:46Z","title_canon_sha256":"d602e8f3baffda24305dc6e088656dc90a7b110ab91f6780b70e3e8a7a9d8989"},"schema_version":"1.0","source":{"id":"1105.2180","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2180","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2180v6","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2180","created_at":"2026-05-18T03:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"7QNDK7LSJORD","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7QNDK7LSJORDUTXL","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7QNDK7LS","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:bd5f996560bcfad74cdfd582da845cf0f01635a1ee9fb8a841129cd9fc0ad6f3","target":"graph","created_at":"2026-05-18T03:32:45Z","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":"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","authors_text":"Chun Liu, Hao Wu, Xiang Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-11T13:18:46Z","title":"On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2180","kind":"arxiv","version":6},"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":"sha256:139be96b766ac37ba13a10a3c0559f8d47fd026adf045b606274966589e75124","target":"record","created_at":"2026-05-18T03:32:45Z","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":"4916822ef4df366a67ec1a93b4aa3051604bc5cd074b41dbf87cf5a93a44f9f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-05-11T13:18:46Z","title_canon_sha256":"d602e8f3baffda24305dc6e088656dc90a7b110ab91f6780b70e3e8a7a9d8989"},"schema_version":"1.0","source":{"id":"1105.2180","kind":"arxiv","version":6}},"canonical_sha256":"fc1a357d724ba23a4eebc45dcae084bb9dfdbb94832fa719a6b01a7e3f8d4595","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc1a357d724ba23a4eebc45dcae084bb9dfdbb94832fa719a6b01a7e3f8d4595","first_computed_at":"2026-05-18T03:32:45.631839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:45.631839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jN94bZfOAng+VOQjZ+KA8didh8lX8UD5sqmU5BoDrHeFy1OO95vqhlljZMn5PtULKcZYdBUWxojngKfbfB7vCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:45.632631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2180","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:139be96b766ac37ba13a10a3c0559f8d47fd026adf045b606274966589e75124","sha256:bd5f996560bcfad74cdfd582da845cf0f01635a1ee9fb8a841129cd9fc0ad6f3"],"state_sha256":"0a14b1b36a8a70a44eb9c9436f1729f06be18e175e5cbd3cf894e2ac567afe9e"}