{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YWTGGGC372NRDG3ZPFBOYIZOLT","short_pith_number":"pith:YWTGGGC3","schema_version":"1.0","canonical_sha256":"c5a663185bfe9b119b797942ec232e5cda82d105408c92f39f56259f90f80681","source":{"kind":"arxiv","id":"1305.0647","version":2},"attestation_state":"computed","paper":{"title":"Navier-Stokes equation and forward-backward stochastic differential system in the Besov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Ana Bela Cruzeiro, Xin Chen, Zhongmin Qian","submitted_at":"2013-05-03T09:14:41Z","abstract_excerpt":"The Navier-Stokes equation on Rd (d greater or equal to 3) formulated on Besov spaces is considered. Using a stochastic forward-backward differential system, the local existence of a unique solution in B_ r, with r > 1 + d is obtained. We also show p,p p the convergence to solutions of the Euler equation when the viscosity tends to zero. Moreover, we prove the local existence of a unique solution in B_ pr,q, with p > 1, 1 greater or equal to q greater or equal to infinity, r > max(1, d); here the maximal time interval depends on p the viscosity."},"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":"1305.0647","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-03T09:14:41Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"2ff10f1239313cdffe53618c0493d1fe66faa6ec2b63f64101b1e7ec60769781","abstract_canon_sha256":"a5021b19f735330d163572cca8988f3abdb8b718719f34a5c57a7c8b5803d254"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:41.139533Z","signature_b64":"n8MF1r49O6f3Szp4903JS8poxL/5aR84cDE6u8auc5+JoJglDKmn9HWd+L+d5YQqqpq4DVJhQs65gsTZQRjuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5a663185bfe9b119b797942ec232e5cda82d105408c92f39f56259f90f80681","last_reissued_at":"2026-05-18T03:24:41.138821Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:41.138821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Navier-Stokes equation and forward-backward stochastic differential system in the Besov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Ana Bela Cruzeiro, Xin Chen, Zhongmin Qian","submitted_at":"2013-05-03T09:14:41Z","abstract_excerpt":"The Navier-Stokes equation on Rd (d greater or equal to 3) formulated on Besov spaces is considered. Using a stochastic forward-backward differential system, the local existence of a unique solution in B_ r, with r > 1 + d is obtained. We also show p,p p the convergence to solutions of the Euler equation when the viscosity tends to zero. Moreover, we prove the local existence of a unique solution in B_ pr,q, with p > 1, 1 greater or equal to q greater or equal to infinity, r > max(1, d); here the maximal time interval depends on p the viscosity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0647","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":"1305.0647","created_at":"2026-05-18T03:24:41.138933+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0647v2","created_at":"2026-05-18T03:24:41.138933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0647","created_at":"2026-05-18T03:24:41.138933+00:00"},{"alias_kind":"pith_short_12","alias_value":"YWTGGGC372NR","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"YWTGGGC372NRDG3Z","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"YWTGGGC3","created_at":"2026-05-18T12:28:09.283467+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/YWTGGGC372NRDG3ZPFBOYIZOLT","json":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT.json","graph_json":"https://pith.science/api/pith-number/YWTGGGC372NRDG3ZPFBOYIZOLT/graph.json","events_json":"https://pith.science/api/pith-number/YWTGGGC372NRDG3ZPFBOYIZOLT/events.json","paper":"https://pith.science/paper/YWTGGGC3"},"agent_actions":{"view_html":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT","download_json":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT.json","view_paper":"https://pith.science/paper/YWTGGGC3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0647&json=true","fetch_graph":"https://pith.science/api/pith-number/YWTGGGC372NRDG3ZPFBOYIZOLT/graph.json","fetch_events":"https://pith.science/api/pith-number/YWTGGGC372NRDG3ZPFBOYIZOLT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT/action/storage_attestation","attest_author":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT/action/author_attestation","sign_citation":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT/action/citation_signature","submit_replication":"https://pith.science/pith/YWTGGGC372NRDG3ZPFBOYIZOLT/action/replication_record"}},"created_at":"2026-05-18T03:24:41.138933+00:00","updated_at":"2026-05-18T03:24:41.138933+00:00"}