{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2PEG5SCZO476ADI6GBQZEL24MB","short_pith_number":"pith:2PEG5SCZ","schema_version":"1.0","canonical_sha256":"d3c86ec859773fe00d1e3061922f5c607f09a039484664415141cc57c6470f08","source":{"kind":"arxiv","id":"1709.09306","version":2},"attestation_state":"computed","paper":{"title":"Strong-Feller property for Navier-Stokes equations driven by space-time white noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Rongchan Zhu, Xiangchan Zhu","submitted_at":"2017-09-27T02:11:39Z","abstract_excerpt":"In this paper we prove strong Feller property for the Markov semigroups associated to the two or three dimensional Navier-Stokes (N-S) equations driven by space-time white noise using the theory of regularity structures introduced by Martin Hairer in [Hai14]. This implies global well-posedness of 2D N-S equation driven by space-time white noise starting from every initial point in $C^\\eta$ for $\\eta\\in (-\\frac{1}{2},0)$."},"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":"1709.09306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-09-27T02:11:39Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"a45e527f23100c9ef2b3197be4bb880b4676b46482cf4c3f13b17d60e6745913","abstract_canon_sha256":"129a867e27aa7dfe367fc4f5cb9f1b6cca3dbfbeb11c7c14e09422862a9b024c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:58.267704Z","signature_b64":"rAKzL6l8nrWl+2fSrd30KKdbqle0ToRLsBOxSiSU407G72UlTDlQxohkvVkkwc7Z+2uGl9NSpn372jCW5tiWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3c86ec859773fe00d1e3061922f5c607f09a039484664415141cc57c6470f08","last_reissued_at":"2026-05-18T00:33:58.266872Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:58.266872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong-Feller property for Navier-Stokes equations driven by space-time white noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Rongchan Zhu, Xiangchan Zhu","submitted_at":"2017-09-27T02:11:39Z","abstract_excerpt":"In this paper we prove strong Feller property for the Markov semigroups associated to the two or three dimensional Navier-Stokes (N-S) equations driven by space-time white noise using the theory of regularity structures introduced by Martin Hairer in [Hai14]. This implies global well-posedness of 2D N-S equation driven by space-time white noise starting from every initial point in $C^\\eta$ for $\\eta\\in (-\\frac{1}{2},0)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09306","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":"1709.09306","created_at":"2026-05-18T00:33:58.267013+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.09306v2","created_at":"2026-05-18T00:33:58.267013+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09306","created_at":"2026-05-18T00:33:58.267013+00:00"},{"alias_kind":"pith_short_12","alias_value":"2PEG5SCZO476","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2PEG5SCZO476ADI6","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2PEG5SCZ","created_at":"2026-05-18T12:30:55.937587+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/2PEG5SCZO476ADI6GBQZEL24MB","json":"https://pith.science/pith/2PEG5SCZO476ADI6GBQZEL24MB.json","graph_json":"https://pith.science/api/pith-number/2PEG5SCZO476ADI6GBQZEL24MB/graph.json","events_json":"https://pith.science/api/pith-number/2PEG5SCZO476ADI6GBQZEL24MB/events.json","paper":"https://pith.science/paper/2PEG5SCZ"},"agent_actions":{"view_html":"https://pith.science/pith/2PEG5SCZO476ADI6GBQZEL24MB","download_json":"https://pith.science/pith/2PEG5SCZO476ADI6GBQZEL24MB.json","view_paper":"https://pith.science/paper/2PEG5SCZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.09306&json=true","fetch_graph":"https://pith.science/api/pith-number/2PEG5SCZO476ADI6GBQZEL24MB/graph.json","fetch_events":"https://pith.science/api/pith-number/2PEG5SCZO476ADI6GBQZEL24MB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2PEG5SCZO476ADI6GBQZEL24MB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2PEG5SCZO476ADI6GBQZEL24MB/action/storage_attestation","attest_author":"https://pith.science/pith/2PEG5SCZO476ADI6GBQZEL24MB/action/author_attestation","sign_citation":"https://pith.science/pith/2PEG5SCZO476ADI6GBQZEL24MB/action/citation_signature","submit_replication":"https://pith.science/pith/2PEG5SCZO476ADI6GBQZEL24MB/action/replication_record"}},"created_at":"2026-05-18T00:33:58.267013+00:00","updated_at":"2026-05-18T00:33:58.267013+00:00"}