{"paper":{"title":"The stability threshold for 2D MHD equations around Couette with general viscosity and magnetic resistivity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fei Wang, Zeren Zhang","submitted_at":"2024-10-27T10:32:47Z","abstract_excerpt":"We address a threshold problem of the Couette flow $(y,0)$ in a uniform magnetic field $(\\beta,0)$ for the 2D MHD equation on $\\mathbb{T}\\times\\mathbb{R}$ with fluid viscosity $\\nu$ and magnetic resistivity $\\mu$. The nonlinear enhanced dissipation and inviscid damping are also established. In particularly, when $0<\\nu\\leq\\mu^3\\leq1$, we get a threshold $\\nu^{\\frac{1}{2}}\\mu^{\\frac{1}{3}}$ in $H^N(N\\geq4)$. When $0<\\mu^3\\leq\\nu\\leq1$, we obtain a threshold $\\min\\{\\nu^{\\frac{1}{2}},\\mu^{\\frac{1}{2}}\\}\\min\\{1,\\nu^{-1}\\mu^{\\frac{1}{3}}\\}$, hence improving the results in [19,14,21]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.20404","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/2410.20404/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"}