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We prove that the flow is linearly stable in the large Reynolds number limit, in two different cases:\n  $\\bullet$ $\\sup_{x\\in[-1,1]} |U\"(x)| + \\sup_{x\\in[-1,1]} |U\"(x)| \\ll\n  \\min_{x\\in[-1,1]}|U^\\prime(x)|$ (nearly Couette flows),\n  $\\bullet$ $U^{\\prime\\prime}\\neq0$ in $[-1,1]$.\n  We assume either no-slip or fixed traction force conditions on the plates, and an arbitrary large ("},"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":"1908.06328","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-17T18:27:01Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4b05c73def9abf2fba883e09e2395ca675006bdb6ec3ed2d08771b7caff56a77","abstract_canon_sha256":"5378782595d6a7f04fc78e1b95bc85f519f10c74297f56904b9e2236629396b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:45:08.635530Z","signature_b64":"rzSjt+c4qeAurtFgifOcv6KHdcOlJYm9GGzUzLF57A6f90pXJqme1QHhcs3FHaCXDhI+VOe1AqWY7NEllcbmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"800baddf580a0143ddcd997e0f64d82f460f6fe39f0c09f09f65535230b9ab1b","last_reissued_at":"2026-07-05T00:45:08.635062Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:45:08.635062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the stability of laminar flows between plates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Bernard Helffer, Yaniv Almog","submitted_at":"2019-08-17T18:27:01Z","abstract_excerpt":"Consider a two-dimensional laminar flow between two plates, so that $(x_1,x_2)\\in {\\mathbb R} \\times[-1,1]$, given by ${\\mathbf v}(x_1,x_2)=(U(x_2),0)$, where\n  $U\\in C^4([-1,1])$ satisfies $U^\\prime\\neq0$ in $[-1,1]$. We prove that the flow is linearly stable in the large Reynolds number limit, in two different cases:\n  $\\bullet$ $\\sup_{x\\in[-1,1]} |U\"(x)| + \\sup_{x\\in[-1,1]} |U\"(x)| \\ll\n  \\min_{x\\in[-1,1]}|U^\\prime(x)|$ (nearly Couette flows),\n  $\\bullet$ $U^{\\prime\\prime}\\neq0$ in $[-1,1]$.\n  We assume either no-slip or fixed traction force conditions on the plates, and an arbitrary large ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06328","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06328/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.06328","created_at":"2026-07-05T00:45:08.635123+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.06328v2","created_at":"2026-07-05T00:45:08.635123+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06328","created_at":"2026-07-05T00:45:08.635123+00:00"},{"alias_kind":"pith_short_12","alias_value":"QAF23X2YBIAU","created_at":"2026-07-05T00:45:08.635123+00:00"},{"alias_kind":"pith_short_16","alias_value":"QAF23X2YBIAUHXON","created_at":"2026-07-05T00:45:08.635123+00:00"},{"alias_kind":"pith_short_8","alias_value":"QAF23X2Y","created_at":"2026-07-05T00:45:08.635123+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/QAF23X2YBIAUHXONTF7A6ZGYF5","json":"https://pith.science/pith/QAF23X2YBIAUHXONTF7A6ZGYF5.json","graph_json":"https://pith.science/api/pith-number/QAF23X2YBIAUHXONTF7A6ZGYF5/graph.json","events_json":"https://pith.science/api/pith-number/QAF23X2YBIAUHXONTF7A6ZGYF5/events.json","paper":"https://pith.science/paper/QAF23X2Y"},"agent_actions":{"view_html":"https://pith.science/pith/QAF23X2YBIAUHXONTF7A6ZGYF5","download_json":"https://pith.science/pith/QAF23X2YBIAUHXONTF7A6ZGYF5.json","view_paper":"https://pith.science/paper/QAF23X2Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.06328&json=true","fetch_graph":"https://pith.science/api/pith-number/QAF23X2YBIAUHXONTF7A6ZGYF5/graph.json","fetch_events":"https://pith.science/api/pith-number/QAF23X2YBIAUHXONTF7A6ZGYF5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QAF23X2YBIAUHXONTF7A6ZGYF5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QAF23X2YBIAUHXONTF7A6ZGYF5/action/storage_attestation","attest_author":"https://pith.science/pith/QAF23X2YBIAUHXONTF7A6ZGYF5/action/author_attestation","sign_citation":"https://pith.science/pith/QAF23X2YBIAUHXONTF7A6ZGYF5/action/citation_signature","submit_replication":"https://pith.science/pith/QAF23X2YBIAUHXONTF7A6ZGYF5/action/replication_record"}},"created_at":"2026-07-05T00:45:08.635123+00:00","updated_at":"2026-07-05T00:45:08.635123+00:00"}