{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YIMVS423DL4Y5G2BUEWOUKLGVT","short_pith_number":"pith:YIMVS423","schema_version":"1.0","canonical_sha256":"c21959735b1af98e9b41a12cea2966ace37459580fc84cda9804fe99241780b4","source":{"kind":"arxiv","id":"1505.00905","version":1},"attestation_state":"computed","paper":{"title":"Regularity of 3D axisymmetric Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daoyuan Fang, Hui Chen, Ting Zhang","submitted_at":"2015-05-05T07:38:20Z","abstract_excerpt":"In this paper, we study the three-dimensional axisymmetric Navier-Stokes system with nonzero swirl. By establishing a new key inequality for the pair $(\\frac{\\omega^{r}}{r},\\frac{\\omega^{\\theta}}{r})$, we get several Prodi-Serrin type regularity criteria based on the angular velocity, $u^\\theta$. Moreover, we obtain the global well-posedness result if the initial angular velocity $u_{0}^{\\theta}$ is appropriate small in the critical space $L^{3}(\\R^{3})$. Furthermore, we also get several Prodi-Serrin type regularity criteria based on one component of the solutions, say $\\omega^3$ or $u^3$."},"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":"1505.00905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-05T07:38:20Z","cross_cats_sorted":[],"title_canon_sha256":"43d181580409635db614be85891322c6ad3e0134d8d217af6caa10284a98097d","abstract_canon_sha256":"875b674c7af385d32370673e376618dde977e9d50165a99d797d4cd65d5361ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:59.643458Z","signature_b64":"TlwpZ7THz5tn/tNhF08LTz3AaTAO2Ocexl6x8Pm1uonp5BdoyC1mMn60+3ZCvF7CruXjbZvk5TrMknYAUhDyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c21959735b1af98e9b41a12cea2966ace37459580fc84cda9804fe99241780b4","last_reissued_at":"2026-05-18T02:16:59.642745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:59.642745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularity of 3D axisymmetric Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daoyuan Fang, Hui Chen, Ting Zhang","submitted_at":"2015-05-05T07:38:20Z","abstract_excerpt":"In this paper, we study the three-dimensional axisymmetric Navier-Stokes system with nonzero swirl. By establishing a new key inequality for the pair $(\\frac{\\omega^{r}}{r},\\frac{\\omega^{\\theta}}{r})$, we get several Prodi-Serrin type regularity criteria based on the angular velocity, $u^\\theta$. Moreover, we obtain the global well-posedness result if the initial angular velocity $u_{0}^{\\theta}$ is appropriate small in the critical space $L^{3}(\\R^{3})$. Furthermore, we also get several Prodi-Serrin type regularity criteria based on one component of the solutions, say $\\omega^3$ or $u^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00905","kind":"arxiv","version":1},"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":"1505.00905","created_at":"2026-05-18T02:16:59.642860+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.00905v1","created_at":"2026-05-18T02:16:59.642860+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00905","created_at":"2026-05-18T02:16:59.642860+00:00"},{"alias_kind":"pith_short_12","alias_value":"YIMVS423DL4Y","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"YIMVS423DL4Y5G2B","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"YIMVS423","created_at":"2026-05-18T12:29:50.041715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2605.16322","citing_title":"A unified Boussinesq--Euler formulation and finite-time blow-up for a Hou--Luo type boundary-jet system","ref_index":8,"is_internal_anchor":true},{"citing_arxiv_id":"2603.26715","citing_title":"2D inviscid Boussinesq equations and 3D axisymmetric Euler equations: (1) A unification ($Em$), (2) Finite-time blow-up of two unified $(1+1)$D systems rigorously derived from ($Em$)","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YIMVS423DL4Y5G2BUEWOUKLGVT","json":"https://pith.science/pith/YIMVS423DL4Y5G2BUEWOUKLGVT.json","graph_json":"https://pith.science/api/pith-number/YIMVS423DL4Y5G2BUEWOUKLGVT/graph.json","events_json":"https://pith.science/api/pith-number/YIMVS423DL4Y5G2BUEWOUKLGVT/events.json","paper":"https://pith.science/paper/YIMVS423"},"agent_actions":{"view_html":"https://pith.science/pith/YIMVS423DL4Y5G2BUEWOUKLGVT","download_json":"https://pith.science/pith/YIMVS423DL4Y5G2BUEWOUKLGVT.json","view_paper":"https://pith.science/paper/YIMVS423","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.00905&json=true","fetch_graph":"https://pith.science/api/pith-number/YIMVS423DL4Y5G2BUEWOUKLGVT/graph.json","fetch_events":"https://pith.science/api/pith-number/YIMVS423DL4Y5G2BUEWOUKLGVT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YIMVS423DL4Y5G2BUEWOUKLGVT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YIMVS423DL4Y5G2BUEWOUKLGVT/action/storage_attestation","attest_author":"https://pith.science/pith/YIMVS423DL4Y5G2BUEWOUKLGVT/action/author_attestation","sign_citation":"https://pith.science/pith/YIMVS423DL4Y5G2BUEWOUKLGVT/action/citation_signature","submit_replication":"https://pith.science/pith/YIMVS423DL4Y5G2BUEWOUKLGVT/action/replication_record"}},"created_at":"2026-05-18T02:16:59.642860+00:00","updated_at":"2026-05-18T02:16:59.642860+00:00"}