{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4YZNAHGRRBY5QBBDDCIOXXLSAX","short_pith_number":"pith:4YZNAHGR","schema_version":"1.0","canonical_sha256":"e632d01cd18871d804231890ebdd7205ebc9f70df5233dbab20a4f569b7dd849","source":{"kind":"arxiv","id":"1510.03561","version":1},"attestation_state":"computed","paper":{"title":"A note on stochastic Navier-Stokes equations with not regular multiplicative noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Benedetta Ferrario, Zdzislaw Brzezniak","submitted_at":"2015-10-13T07:38:47Z","abstract_excerpt":"We consider the Navier-Stokes equations in $\\mathbb R^d$ ($d=2,3$) with a stochastic forcing term which is white noise in time and coloured in space; the spatial covariance of the noise is not too regular, so It\\^o calculus cannot be applied in the space of finite energy vector fields. We prove existence of weak solutions for $d=2,3$ and pathwise uniqueness for $d=2$."},"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":"1510.03561","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-13T07:38:47Z","cross_cats_sorted":[],"title_canon_sha256":"fa868b928a1ef69e63840f606774c482cf47bb658c48795d86058a8c74e0fb9c","abstract_canon_sha256":"47fffc2192fbe04f536b4227b289ba0cd0a6ee8f5de614c956cb5897b1bf9ab7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:16.813198Z","signature_b64":"BVdLWW0s0fxXNcPAzXDyausgxU6UaetAjTfwGjlDEVV7ow9qBPQqpBPREYQXy3UBVu6vq+x2AW/nkLnq5fwcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e632d01cd18871d804231890ebdd7205ebc9f70df5233dbab20a4f569b7dd849","last_reissued_at":"2026-05-18T01:30:16.812686Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:16.812686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on stochastic Navier-Stokes equations with not regular multiplicative noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Benedetta Ferrario, Zdzislaw Brzezniak","submitted_at":"2015-10-13T07:38:47Z","abstract_excerpt":"We consider the Navier-Stokes equations in $\\mathbb R^d$ ($d=2,3$) with a stochastic forcing term which is white noise in time and coloured in space; the spatial covariance of the noise is not too regular, so It\\^o calculus cannot be applied in the space of finite energy vector fields. We prove existence of weak solutions for $d=2,3$ and pathwise uniqueness for $d=2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03561","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":"1510.03561","created_at":"2026-05-18T01:30:16.812761+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.03561v1","created_at":"2026-05-18T01:30:16.812761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03561","created_at":"2026-05-18T01:30:16.812761+00:00"},{"alias_kind":"pith_short_12","alias_value":"4YZNAHGRRBY5","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4YZNAHGRRBY5QBBD","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4YZNAHGR","created_at":"2026-05-18T12:29:05.191682+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/4YZNAHGRRBY5QBBDDCIOXXLSAX","json":"https://pith.science/pith/4YZNAHGRRBY5QBBDDCIOXXLSAX.json","graph_json":"https://pith.science/api/pith-number/4YZNAHGRRBY5QBBDDCIOXXLSAX/graph.json","events_json":"https://pith.science/api/pith-number/4YZNAHGRRBY5QBBDDCIOXXLSAX/events.json","paper":"https://pith.science/paper/4YZNAHGR"},"agent_actions":{"view_html":"https://pith.science/pith/4YZNAHGRRBY5QBBDDCIOXXLSAX","download_json":"https://pith.science/pith/4YZNAHGRRBY5QBBDDCIOXXLSAX.json","view_paper":"https://pith.science/paper/4YZNAHGR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.03561&json=true","fetch_graph":"https://pith.science/api/pith-number/4YZNAHGRRBY5QBBDDCIOXXLSAX/graph.json","fetch_events":"https://pith.science/api/pith-number/4YZNAHGRRBY5QBBDDCIOXXLSAX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4YZNAHGRRBY5QBBDDCIOXXLSAX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4YZNAHGRRBY5QBBDDCIOXXLSAX/action/storage_attestation","attest_author":"https://pith.science/pith/4YZNAHGRRBY5QBBDDCIOXXLSAX/action/author_attestation","sign_citation":"https://pith.science/pith/4YZNAHGRRBY5QBBDDCIOXXLSAX/action/citation_signature","submit_replication":"https://pith.science/pith/4YZNAHGRRBY5QBBDDCIOXXLSAX/action/replication_record"}},"created_at":"2026-05-18T01:30:16.812761+00:00","updated_at":"2026-05-18T01:30:16.812761+00:00"}