{"paper":{"title":"Low-regularity Schr\\\"odinger map flow on high-dimensional periodic domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Li Tu, Yi Zhou","submitted_at":"2026-06-11T05:33:11Z","abstract_excerpt":"We study the initial-value problem for the Schr\\\"odinger map flow from flat torus $\\mathbb{T}^d$ into compact K\\\"ahler manifold $\\mathcal{N}$. When $d \\geq 3$ and $\\mathcal{N} = \\mathbb{S}^2$, we establish local well-posedness in $H^{\\sigma}_x$ with $\\sigma > d/2 + 1/2$. In this case, the evolution equation for the gradient of the solution reduces to a certain semilinear nonlinear Schr\\\"odinger equation (also known as modified Schr\\\"odinger map flow) when formulated in orthonormal frames. For general compact K\\\"ahler targets, we only obtain local well-posedness in $H^{\\sigma}_x$ with $ \\sigma "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12926","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/2606.12926/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"}