{"paper":{"title":"Sharp non-uniqueness of weak solutions to 2D magnetohydrodynamic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Weikui Ye, Yao Nie","submitted_at":"2026-05-24T14:18:28Z","abstract_excerpt":"In this paper, we prove that weak solutions to the 2D viscous and resistive magnetohydrodynamic (MHD) equations are non-unique in $L^2_t L^p(\\mathbb{R}^2) \\cap L^1_t W^{1,p}(\\mathbb{R}^2)$ for given any $1\\le p<\\infty$, showing the sharpness of the Ladyzhenskaya--Prodi--Serrin condition at the endpoint $(2,\\infty)$ and the solutions live on the borderline of the Beale--Kato--Majda criterion. To the best of our knowledge, this is the first non-uniqueness result for the 2D viscous and resistive MHD system. As byproducts, we also obtain non-uniqueness for the Navier--Stokes equations in $L^2_t L^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25097","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/2605.25097/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"}