{"paper":{"title":"Local well-posedness for the two-and-a-half-dimensional EMHD system with split fractional dissipation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qirui Peng","submitted_at":"2026-05-20T07:35:30Z","abstract_excerpt":"We study the $2\\frac12$-dimensional electron magnetohydrodynamics (EMHD) system on $\\mathbb T^2$ with componentwise fractional dissipation: $\\partial_t a+a_yb_x-a_xb_y=-\\Lambda^\\alpha a$ and $\\partial_t b-a_y\\Delta a_x+a_x\\Delta a_y=-\\Lambda^\\beta b$, where $0<\\alpha,\\beta<2$. This system is a $2\\frac12$-dimensional reduction of the magnetic equation in Hall--MHD/EMHD under the ansatz $B=\\nabla\\times(ae_z)+be_z$. We prove local well-posedness for initial data $(a_0,b_0)\\in H^{s+1}(\\mathbb T^2)\\times H^s(\\mathbb T^2)$ with $s\\geq 2-\\varepsilon$, provided that $\\alpha+\\beta>2$. Thus neither comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20845","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/2605.20845/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"}