{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QRKW3R3A7YFJTTARZ2H4MRHU27","short_pith_number":"pith:QRKW3R3A","schema_version":"1.0","canonical_sha256":"84556dc760fe0a99cc11ce8fc644f4d7f30912520a796448bf584ff69881252c","source":{"kind":"arxiv","id":"1112.4566","version":2},"attestation_state":"computed","paper":{"title":"Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jihoon Lee, Kyungkeun Kang, Myeongju Chae","submitted_at":"2011-12-20T04:21:24Z","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"},"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":"1112.4566","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-20T04:21:24Z","cross_cats_sorted":[],"title_canon_sha256":"fb44443862133166f96a294c58e3bae67f292cc3c71c10ccab60e8db1e479bef","abstract_canon_sha256":"132f49ea487897f77df1d68f644d3e8d384d4f3e8ded6023f98e7e17406a54bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:01.602194Z","signature_b64":"vhXt04dxN0nVhpfjHpTLIytgCrZVcB8Kj3hWACa3RFU0aDZDAvr55P3dLHypp4KfGxSxczDO78/FOcLxAAdkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84556dc760fe0a99cc11ce8fc644f4d7f30912520a796448bf584ff69881252c","last_reissued_at":"2026-05-18T04:02:01.601434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:01.601434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jihoon Lee, Kyungkeun Kang, Myeongju Chae","submitted_at":"2011-12-20T04:21:24Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4566","kind":"arxiv","version":2},"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":"1112.4566","created_at":"2026-05-18T04:02:01.601560+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.4566v2","created_at":"2026-05-18T04:02:01.601560+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4566","created_at":"2026-05-18T04:02:01.601560+00:00"},{"alias_kind":"pith_short_12","alias_value":"QRKW3R3A7YFJ","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QRKW3R3A7YFJTTAR","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QRKW3R3A","created_at":"2026-05-18T12:26:39.201973+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/QRKW3R3A7YFJTTARZ2H4MRHU27","json":"https://pith.science/pith/QRKW3R3A7YFJTTARZ2H4MRHU27.json","graph_json":"https://pith.science/api/pith-number/QRKW3R3A7YFJTTARZ2H4MRHU27/graph.json","events_json":"https://pith.science/api/pith-number/QRKW3R3A7YFJTTARZ2H4MRHU27/events.json","paper":"https://pith.science/paper/QRKW3R3A"},"agent_actions":{"view_html":"https://pith.science/pith/QRKW3R3A7YFJTTARZ2H4MRHU27","download_json":"https://pith.science/pith/QRKW3R3A7YFJTTARZ2H4MRHU27.json","view_paper":"https://pith.science/paper/QRKW3R3A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.4566&json=true","fetch_graph":"https://pith.science/api/pith-number/QRKW3R3A7YFJTTARZ2H4MRHU27/graph.json","fetch_events":"https://pith.science/api/pith-number/QRKW3R3A7YFJTTARZ2H4MRHU27/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QRKW3R3A7YFJTTARZ2H4MRHU27/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QRKW3R3A7YFJTTARZ2H4MRHU27/action/storage_attestation","attest_author":"https://pith.science/pith/QRKW3R3A7YFJTTARZ2H4MRHU27/action/author_attestation","sign_citation":"https://pith.science/pith/QRKW3R3A7YFJTTARZ2H4MRHU27/action/citation_signature","submit_replication":"https://pith.science/pith/QRKW3R3A7YFJTTARZ2H4MRHU27/action/replication_record"}},"created_at":"2026-05-18T04:02:01.601560+00:00","updated_at":"2026-05-18T04:02:01.601560+00:00"}