{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:R6NLAUUXGDX4OXFAQO3CE2UNI2","short_pith_number":"pith:R6NLAUUX","schema_version":"1.0","canonical_sha256":"8f9ab0529730efc75ca083b6226a8d46a5c306ca8607c7ec4757affff4b320e2","source":{"kind":"arxiv","id":"1402.1395","version":1},"attestation_state":"computed","paper":{"title":"Spectral instability of symmetric shear flows in a two-dimensional channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Emmanuel Grenier, Toan Nguyen, Yan Guo","submitted_at":"2014-02-06T16:26:58Z","abstract_excerpt":"This paper concerns spectral instability of shear flows in the incompressible Navier-Stokes equations with sufficiently large Reynolds number: $R\\to \\infty$. It is well-documented in the physical literature, going back to Heisenberg, C.C. Lin, Tollmien, Drazin and Reid, that generic plane shear profiles other than the linear Couette flow are linearly unstable for sufficiently large Reynolds number. In this work, we provide a complete mathematical proof of these physical results. In the case of a symmetric channel flow, our analysis gives exact unstable eigenvalues and eigenfunctions, showing t"},"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":"1402.1395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-06T16:26:58Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"687e9b186cedfd31cee63a890a8de0f38758088f0034a935fd89655ede8f4a98","abstract_canon_sha256":"d256e46c321396b14c98fdbb7783da1fc2127f7c032aa4fdce82b13f9c72edae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:59.111970Z","signature_b64":"X4um3IQTON4aSszUef4+LS6MvRSE53kBQqJZ1cSo2d/tDRKPf9dRnLthdG5uuZXjXmUzi8cjGlRHctfd0WeKBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f9ab0529730efc75ca083b6226a8d46a5c306ca8607c7ec4757affff4b320e2","last_reissued_at":"2026-05-18T02:59:59.111154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:59.111154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral instability of symmetric shear flows in a two-dimensional channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Emmanuel Grenier, Toan Nguyen, Yan Guo","submitted_at":"2014-02-06T16:26:58Z","abstract_excerpt":"This paper concerns spectral instability of shear flows in the incompressible Navier-Stokes equations with sufficiently large Reynolds number: $R\\to \\infty$. It is well-documented in the physical literature, going back to Heisenberg, C.C. Lin, Tollmien, Drazin and Reid, that generic plane shear profiles other than the linear Couette flow are linearly unstable for sufficiently large Reynolds number. In this work, we provide a complete mathematical proof of these physical results. In the case of a symmetric channel flow, our analysis gives exact unstable eigenvalues and eigenfunctions, showing t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1395","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":"1402.1395","created_at":"2026-05-18T02:59:59.111288+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.1395v1","created_at":"2026-05-18T02:59:59.111288+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.1395","created_at":"2026-05-18T02:59:59.111288+00:00"},{"alias_kind":"pith_short_12","alias_value":"R6NLAUUXGDX4","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"R6NLAUUXGDX4OXFA","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"R6NLAUUX","created_at":"2026-05-18T12:28:46.137349+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/R6NLAUUXGDX4OXFAQO3CE2UNI2","json":"https://pith.science/pith/R6NLAUUXGDX4OXFAQO3CE2UNI2.json","graph_json":"https://pith.science/api/pith-number/R6NLAUUXGDX4OXFAQO3CE2UNI2/graph.json","events_json":"https://pith.science/api/pith-number/R6NLAUUXGDX4OXFAQO3CE2UNI2/events.json","paper":"https://pith.science/paper/R6NLAUUX"},"agent_actions":{"view_html":"https://pith.science/pith/R6NLAUUXGDX4OXFAQO3CE2UNI2","download_json":"https://pith.science/pith/R6NLAUUXGDX4OXFAQO3CE2UNI2.json","view_paper":"https://pith.science/paper/R6NLAUUX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.1395&json=true","fetch_graph":"https://pith.science/api/pith-number/R6NLAUUXGDX4OXFAQO3CE2UNI2/graph.json","fetch_events":"https://pith.science/api/pith-number/R6NLAUUXGDX4OXFAQO3CE2UNI2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R6NLAUUXGDX4OXFAQO3CE2UNI2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R6NLAUUXGDX4OXFAQO3CE2UNI2/action/storage_attestation","attest_author":"https://pith.science/pith/R6NLAUUXGDX4OXFAQO3CE2UNI2/action/author_attestation","sign_citation":"https://pith.science/pith/R6NLAUUXGDX4OXFAQO3CE2UNI2/action/citation_signature","submit_replication":"https://pith.science/pith/R6NLAUUXGDX4OXFAQO3CE2UNI2/action/replication_record"}},"created_at":"2026-05-18T02:59:59.111288+00:00","updated_at":"2026-05-18T02:59:59.111288+00:00"}