{"paper":{"title":"The half-wave maps equation on $\\mathbb{T}$: Global well-posedness in $H^{1/2}$ and almost periodicity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Patrick G\\'erard","submitted_at":"2026-02-24T13:31:05Z","abstract_excerpt":"We consider the half-wave maps equation $$ \\partial_t \\mathbf{u} = \\mathbf{u} \\times |D| \\mathbf{u} $$ for $\\mathbf{u} : \\mathbb{R} \\times \\mathbb{T} \\to \\mathbb{S}^2$, where $\\mathbb{T}=\\mathbb{R}/2 \\pi \\mathbb{Z}$ is the one-dimensional torus and $\\mathbb{S}^2 \\subset \\mathbb{R}^3$ denotes the unit sphere. By extension from rational initial data, we construct a unique and continuous flow map for data in the critical energy space $H^{1/2}(\\mathbb{T}; \\mathbb{S}^2)$. Moreover, we show almost periodicity in time of these solutions. For the dense subset of rational initial data, we establish qua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.20895","kind":"arxiv","version":3},"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/2602.20895/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"}