{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:AHKNS4S2BCPSPFR734CDP4IWMC","short_pith_number":"pith:AHKNS4S2","schema_version":"1.0","canonical_sha256":"01d4d9725a089f27963fdf0437f11660b61419d1b2c375dde1dd72f1d020904f","source":{"kind":"arxiv","id":"1808.08736","version":1},"attestation_state":"computed","paper":{"title":"Transition threshold for the 2-D Couette flow in a finite channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongyi Wei, Qi Chen, Te Li, Zhifei Zhang","submitted_at":"2018-08-27T08:48:40Z","abstract_excerpt":"In this paper, we study the transition threshold problem for the 2-D Navier-Stokes equations around the Couette flow $(y,0)$ at large Reynolds number $Re$ in a finite channel. We develop a systematic method to establish the resolvent estimates of the linearized operator and space-time estimates of the linearized Navier-Stokes equations. In particular, three kinds of important effects: enhanced dissipation, inviscid damping and boundary layer, are integrated into the space-time estimates in a sharp form. As an application, we prove that if the initial velocity $v_0$ satisfies $\\|v_0-(y, 0)\\|_{H"},"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":"1808.08736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-27T08:48:40Z","cross_cats_sorted":[],"title_canon_sha256":"16ceb8933c3f2a83362eddb512140ad5c0f31527c69672916e30f6d6db692e15","abstract_canon_sha256":"078d6701526878cad967aab117812d7bff191decefa908907ce8e5d57e874a37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:13.417649Z","signature_b64":"FaEsHOJgK23qyK3/A4bkKfsiOhZ4RCIm45fYcwguevgwK4UiwhkP+UuGen9B140gQWUMWKRtRjZc127+rr79BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01d4d9725a089f27963fdf0437f11660b61419d1b2c375dde1dd72f1d020904f","last_reissued_at":"2026-05-18T00:07:13.416986Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:13.416986Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transition threshold for the 2-D Couette flow in a finite channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongyi Wei, Qi Chen, Te Li, Zhifei Zhang","submitted_at":"2018-08-27T08:48:40Z","abstract_excerpt":"In this paper, we study the transition threshold problem for the 2-D Navier-Stokes equations around the Couette flow $(y,0)$ at large Reynolds number $Re$ in a finite channel. We develop a systematic method to establish the resolvent estimates of the linearized operator and space-time estimates of the linearized Navier-Stokes equations. In particular, three kinds of important effects: enhanced dissipation, inviscid damping and boundary layer, are integrated into the space-time estimates in a sharp form. As an application, we prove that if the initial velocity $v_0$ satisfies $\\|v_0-(y, 0)\\|_{H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08736","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":"1808.08736","created_at":"2026-05-18T00:07:13.417083+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.08736v1","created_at":"2026-05-18T00:07:13.417083+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08736","created_at":"2026-05-18T00:07:13.417083+00:00"},{"alias_kind":"pith_short_12","alias_value":"AHKNS4S2BCPS","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AHKNS4S2BCPSPFR7","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AHKNS4S2","created_at":"2026-05-18T12:32:13.499390+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/AHKNS4S2BCPSPFR734CDP4IWMC","json":"https://pith.science/pith/AHKNS4S2BCPSPFR734CDP4IWMC.json","graph_json":"https://pith.science/api/pith-number/AHKNS4S2BCPSPFR734CDP4IWMC/graph.json","events_json":"https://pith.science/api/pith-number/AHKNS4S2BCPSPFR734CDP4IWMC/events.json","paper":"https://pith.science/paper/AHKNS4S2"},"agent_actions":{"view_html":"https://pith.science/pith/AHKNS4S2BCPSPFR734CDP4IWMC","download_json":"https://pith.science/pith/AHKNS4S2BCPSPFR734CDP4IWMC.json","view_paper":"https://pith.science/paper/AHKNS4S2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.08736&json=true","fetch_graph":"https://pith.science/api/pith-number/AHKNS4S2BCPSPFR734CDP4IWMC/graph.json","fetch_events":"https://pith.science/api/pith-number/AHKNS4S2BCPSPFR734CDP4IWMC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AHKNS4S2BCPSPFR734CDP4IWMC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AHKNS4S2BCPSPFR734CDP4IWMC/action/storage_attestation","attest_author":"https://pith.science/pith/AHKNS4S2BCPSPFR734CDP4IWMC/action/author_attestation","sign_citation":"https://pith.science/pith/AHKNS4S2BCPSPFR734CDP4IWMC/action/citation_signature","submit_replication":"https://pith.science/pith/AHKNS4S2BCPSPFR734CDP4IWMC/action/replication_record"}},"created_at":"2026-05-18T00:07:13.417083+00:00","updated_at":"2026-05-18T00:07:13.417083+00:00"}