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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.20845","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-05-20T07:35:30Z","cross_cats_sorted":[],"title_canon_sha256":"33f87444a2baca1cee1e2fb576844e59901de4244aa1bd8f6afec5d142312804","abstract_canon_sha256":"c0dbc60328664a9f45130741ab89500f490da023f3f28749b0c2f11332a6d4bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:24.269864Z","signature_b64":"p4DsVG9NJqll1ZYDfsjTEW/QeofIOqs9YIL20+NnpqYv/M1zyEuMtaE9b410Yl7vgZ12ioiiBiULWZISwbG4AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76cbfce7347c1ac4395daf412faeeaadf483608cd335a7cd9bf821ccdaa318ca","last_reissued_at":"2026-05-21T01:05:24.269275Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:24.269275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\alpha+\\beta>2$. 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