{"paper":{"title":"A Study on the Well-Posedness of 1D Energy-Critical Half-Wave Maps Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gaspard Ohlmann","submitted_at":"2023-10-20T12:10:30Z","abstract_excerpt":"In this article, we study the well-posedness of the energy-critical half-wave maps equation (HWM) in dimension $1$. The half-wave maps equation emerges from the continuum limit of the Haldane Shastry spin chains and has been shown to arise as the continuum limit of Calogero-Moser classical spin systems. In higher dimension $d\\geq 5$, it has been shown that (HWM) is well-posed by Krieger and Sire. This result has been improved by Krieger and Kiesenhofer to $d = 4$ but the Strichartz estimate on which the argument is built no longer holds for smaller dimensions. A Lax-pair structure has been rev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.13442","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/2310.13442/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"}