{"paper":{"title":"Long-wave instability of periodic shear flows with constant magnetic field for the 2D resistive MHD equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Claudia Pe\\~na, Luca Franzoi, Riccardo Montalto, Roberto Feola","submitted_at":"2026-07-28T15:16:01Z","abstract_excerpt":"We investigate the long-wave linear stability and instability of the two-dimensional viscous, resistive Magnetohydrodynamic (MHD) equations, in vorticity-current formulation, on the periodic domain ${\\mathbb T}_\\alpha\\times {\\mathbb T} = \\Big( {\\mathbb R}/(\\frac{2 \\pi}{\\alpha} {\\mathbb Z}) \\times {\\mathbb R}/(2 \\pi {\\mathbb Z}) \\Big)$, around a periodic shear flow $(U(y),0)$ coupled with a constant background magnetic field ${\\bf b}=({\\rm b}_1,{\\rm b}_2)$. It is a non-trivial extension of a recent paper for the Navier-Stokes equations by Colombo, Dolce, Montalto & Ventura to the MHD setting in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25836","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/2607.25836/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"}