{"paper":{"title":"The stability threshold for 3D MHD equations around Couette with rationally aligned magnetic field","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fei Wang, Lingda Xu, Zeren Zhang","submitted_at":"2025-05-26T11:00:11Z","abstract_excerpt":"We address a stability threshold problem of the Couette flow $(y,0,0)$ in a uniform magnetic fleld $\\alpha(\\sigma,0,1)$ with $\\sigma\\in\\mathbb{Q}$ for the 3D MHD equations on $\\mathbb{T}\\times\\mathbb{R}\\times\\mathbb{T}$. Previously, the authors in \\cite{L20,RZZ25} obtained the threshold $\\gamma=1$ for $\\sigma\\in\\mathbb{R}\\backslash\\mathbb{Q}$ satisfying a generic Diophantine condition, where they also proved $\\gamma = 4/3$ for a general $\\sigma\\in\\mathbb{R}$. In the present paper, we obtain the threshold $\\gamma=1$ in $H^N(N>13/2)$, hence improving the above results when $\\sigma$ is a rational"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19822","kind":"arxiv","version":3},"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/2505.19822/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"}