{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BTCLRD6A65M44GMKZWII536LAF","short_pith_number":"pith:BTCLRD6A","schema_version":"1.0","canonical_sha256":"0cc4b88fc0f759ce198acd908eefcb0175b486316784d686c800fdadab9d5f8c","source":{"kind":"arxiv","id":"1511.03523","version":2},"attestation_state":"computed","paper":{"title":"Asymptotic expansion in Gevrey spaces for solutions of Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luan T. Hoang, Vincent R. Martinez","submitted_at":"2015-11-11T14:58:33Z","abstract_excerpt":"In this paper, we study the asymptotic behavior of solutions to the three-dimensional incompressible Navier-Stokes equations (NSE) with periodic boundary conditions and potential body forces. In particular, we prove that the Foias-Saut asymptotic expansion for the regular solutions of the NSE in fact holds in {\\textit{all Gevrey classes}}. This strengthens the previous result obtained in Sobolev spaces by Foias-Saut. By using the Gevrey-norm technique of Foias-Temam, the proof of our improved result simplifies the original argument of Foias-Saut, thereby, increasing its adaptability to other d"},"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":"1511.03523","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-11T14:58:33Z","cross_cats_sorted":[],"title_canon_sha256":"6a0b809068aecda502edb08cdbcf89a31343fade26fd5cc2639f03bdd1d6ba58","abstract_canon_sha256":"287b273af7d10ab263a88733a5003a2f1b6ff003a0f53ba918e7942434f5eae3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:26.220890Z","signature_b64":"Bg+xhBnw9t/OmmHSMMe3a1YYl4t+uEBEs1K0nxdNek+hoUpv9w3fAQ4j6pD/KnGkLRh2H6jtTaUxERXkaCqwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cc4b88fc0f759ce198acd908eefcb0175b486316784d686c800fdadab9d5f8c","last_reissued_at":"2026-05-18T00:45:26.220380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:26.220380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic expansion in Gevrey spaces for solutions of Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luan T. Hoang, Vincent R. Martinez","submitted_at":"2015-11-11T14:58:33Z","abstract_excerpt":"In this paper, we study the asymptotic behavior of solutions to the three-dimensional incompressible Navier-Stokes equations (NSE) with periodic boundary conditions and potential body forces. In particular, we prove that the Foias-Saut asymptotic expansion for the regular solutions of the NSE in fact holds in {\\textit{all Gevrey classes}}. This strengthens the previous result obtained in Sobolev spaces by Foias-Saut. By using the Gevrey-norm technique of Foias-Temam, the proof of our improved result simplifies the original argument of Foias-Saut, thereby, increasing its adaptability to other d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03523","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":"1511.03523","created_at":"2026-05-18T00:45:26.220446+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.03523v2","created_at":"2026-05-18T00:45:26.220446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03523","created_at":"2026-05-18T00:45:26.220446+00:00"},{"alias_kind":"pith_short_12","alias_value":"BTCLRD6A65M4","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BTCLRD6A65M44GMK","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BTCLRD6A","created_at":"2026-05-18T12:29:14.074870+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/BTCLRD6A65M44GMKZWII536LAF","json":"https://pith.science/pith/BTCLRD6A65M44GMKZWII536LAF.json","graph_json":"https://pith.science/api/pith-number/BTCLRD6A65M44GMKZWII536LAF/graph.json","events_json":"https://pith.science/api/pith-number/BTCLRD6A65M44GMKZWII536LAF/events.json","paper":"https://pith.science/paper/BTCLRD6A"},"agent_actions":{"view_html":"https://pith.science/pith/BTCLRD6A65M44GMKZWII536LAF","download_json":"https://pith.science/pith/BTCLRD6A65M44GMKZWII536LAF.json","view_paper":"https://pith.science/paper/BTCLRD6A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.03523&json=true","fetch_graph":"https://pith.science/api/pith-number/BTCLRD6A65M44GMKZWII536LAF/graph.json","fetch_events":"https://pith.science/api/pith-number/BTCLRD6A65M44GMKZWII536LAF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BTCLRD6A65M44GMKZWII536LAF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BTCLRD6A65M44GMKZWII536LAF/action/storage_attestation","attest_author":"https://pith.science/pith/BTCLRD6A65M44GMKZWII536LAF/action/author_attestation","sign_citation":"https://pith.science/pith/BTCLRD6A65M44GMKZWII536LAF/action/citation_signature","submit_replication":"https://pith.science/pith/BTCLRD6A65M44GMKZWII536LAF/action/replication_record"}},"created_at":"2026-05-18T00:45:26.220446+00:00","updated_at":"2026-05-18T00:45:26.220446+00:00"}