{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QRKW3R3A7YFJTTARZ2H4MRHU27","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":"132f49ea487897f77df1d68f644d3e8d384d4f3e8ded6023f98e7e17406a54bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-20T04:21:24Z","title_canon_sha256":"fb44443862133166f96a294c58e3bae67f292cc3c71c10ccab60e8db1e479bef"},"schema_version":"1.0","source":{"id":"1112.4566","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4566","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4566v2","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4566","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"pith_short_12","alias_value":"QRKW3R3A7YFJ","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QRKW3R3A7YFJTTAR","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QRKW3R3A","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:9581e6bf2ef64e17c23a248ec6adad8285f005e87085b34c0dbdf4f17b696a33","target":"graph","created_at":"2026-05-18T04:02:01Z","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":"We consider a system coupling the parabolic-parabolic Keller-Segel equations to the in- compressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria. For two dimensional Navier-Stokes-Keller-Segel equations, regular solutions constructed locally in time are, in reality, extended globally under some assumptions pertinent to experimental observation in [20] on the consumption rate and chemotactic sensitivity. We also show the existence of global weak solutions in spatially three dimensions with r","authors_text":"Jihoon Lee, Kyungkeun Kang, Myeongju Chae","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-20T04:21:24Z","title":"Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4566","kind":"arxiv","version":2},"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":"sha256:6c83b741eb0ae18aad7c1f62a93ef27bd5c0c43d5b7697d5cf3c5aafb9e5b9c9","target":"record","created_at":"2026-05-18T04:02:01Z","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":"132f49ea487897f77df1d68f644d3e8d384d4f3e8ded6023f98e7e17406a54bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-20T04:21:24Z","title_canon_sha256":"fb44443862133166f96a294c58e3bae67f292cc3c71c10ccab60e8db1e479bef"},"schema_version":"1.0","source":{"id":"1112.4566","kind":"arxiv","version":2}},"canonical_sha256":"84556dc760fe0a99cc11ce8fc644f4d7f30912520a796448bf584ff69881252c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84556dc760fe0a99cc11ce8fc644f4d7f30912520a796448bf584ff69881252c","first_computed_at":"2026-05-18T04:02:01.601434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:01.601434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vhXt04dxN0nVhpfjHpTLIytgCrZVcB8Kj3hWACa3RFU0aDZDAvr55P3dLHypp4KfGxSxczDO78/FOcLxAAdkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:01.602194Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4566","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c83b741eb0ae18aad7c1f62a93ef27bd5c0c43d5b7697d5cf3c5aafb9e5b9c9","sha256:9581e6bf2ef64e17c23a248ec6adad8285f005e87085b34c0dbdf4f17b696a33"],"state_sha256":"7be24fd956ab9fcb4001d533a86e0a9d194a864f5c1b8e7f42fe503d1baebf4e"}