{"paper":{"title":"Stability threshold of Couette flow for 3D Boussinesq system in Sobolev spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lili Wang, Shikun Cui, Wendong Wang","submitted_at":"2025-04-23T04:09:55Z","abstract_excerpt":"In this paper, we investigate the nonlinear stability and transition threshold for the 3D Boussinesq system in Sobolev space under the high Reynolds number and small thermal diffusion in $\\mathbb{T}\\times\\mathbb{R}\\times\\mathbb{T} $. It is proved that if the initial velocity $v_{\\rm in}$ and the initial temperature $ \\theta_{\\rm in} $ satisfy $ \\|v_{\\rm in}-(y,0,0)\\|_{H^{2}}\\leq \\varepsilon\\nu, \\|\\theta_{\\rm in}\\|_{H^{2}}\\leq \\varepsilon\\nu^{2} $, respectively for some $ \\varepsilon>0 $ independent of the Reynolds number or thermal diffusion, then the solutions of 3D Boussinesq system are glob"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16401","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.16401/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"}