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Using the pseudospectral bound and the wave operator method introduced in [LWZ], we prove the sharp enhanced dissipation rate for the linearized Navier-Stokes equations. As an application, we prove that if the initial velocity satisfies $\\big\\| U_0-\\big(k_f^{-2}\\sin(k_fy),0,0\\big)\\big\\|_{H^2}\\le c\\nu^{\\frac{7}{4}}$ ($\\nu$ the viscosity coefficient) and $k_f\\in (0,1)$, then the solution does not transition away from the Kolmogorov flow."},"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":"1801.05645","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-01-17T12:55:09Z","cross_cats_sorted":[],"title_canon_sha256":"55e346b75ccdacf0ccb17c929cca63f628b0f1a29a84fdcb83ba1429bca5037a","abstract_canon_sha256":"4276bdc71861450bc1d888711d092c082bf2472bd20f4d3c4ad41c874021f5e4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:40.577253Z","signature_b64":"SEApzt/OOZ6fJELqo+qMUhmJvwp7fPCtoOxUcxiygHdiFOHITTM4hVX/4rL9evUl904xdN+vMpAlV9IuSeeuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44104da445f26201ec2118515d7cad8e7f6f548c846f1c0ee5c2e4bc7672469d","last_reissued_at":"2026-05-18T00:25:40.576745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:40.576745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pseudospectral bound and transition threshold for the 3D Kolmogorov flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongyi Wei, Te Li, Zhifei Zhang","submitted_at":"2018-01-17T12:55:09Z","abstract_excerpt":"In this paper, we establish the pseudospectral bound for the linearized operator of the Navier-Stokes equations around the 3D Kolmogorov flow. 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