{"paper":{"title":"Stability threshold of Couette flow for Boussinesq equations in $\\mathbb{R}^2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guoxu Yang, Wendong Wang, Yubo Chen","submitted_at":"2025-08-16T04:46:48Z","abstract_excerpt":"This paper establishes the asymptotic stability threshold for the Couette flow $(y,0)$ under the 2D Boussinesq system in $\\mathbb{R}^2$. It was proved that for initial perturbations in Sobolev spaces with controlled low horizontal frequencies, the stability threshold is at most $\\left\\{\\frac{1}{3}+, \\frac{2}{3}+\\right\\}$, extending the known threshold results from the periodic case $\\mathbb{T}_x \\times \\mathbb{R}_y$ to the whole space. The core innovations are twofold: First, the $\\langle D_x^{-1} \\rangle$ control on the initial data simultaneously resolves horizontal frequency singularities a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.11908","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/2508.11908/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"}