{"paper":{"title":"Finite-time blow-up solutions for the Calogero--Sutherland derivative NLS","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Xi Chen","submitted_at":"2026-05-27T17:48:11Z","abstract_excerpt":"We construct an explicit family of smooth finite-time blow-up solutions for the focusing Calogero--Sutherland derivative NLS given by $$ i \\partial_t u = -\\partial_x^2 u - 2 D \\Pi(|u|^2) u \\quad \\mbox{with} \\quad (t,x) \\in \\mathbb{R} \\times \\mathbb{T} , $$ where $D=-i \\partial_x$ and $\\Pi$ denotes the Cauchy--Szeg\\H{o} projector. This is a mass-critical NLS-type equation with a Lax pair structure. The Cauchy problem is global well-posed in the class of Hardy-Sobolev spaces $H^s_+(\\mathbb{T})=L^2_+(\\mathbb{T}) \\cap H^s(\\mathbb{T})$ for small $L^2$-mass $\\| u_0 \\|_{L^2}^2 < 1$ as recently proven"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28789","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/2605.28789/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"}