{"paper":{"title":"Well- and Ill-posedness of the Cauchy problem for derivative fractional nonlinear Schr\\\"odinger equations on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mamoru Okamoto, Takamori Kato, Toshiki Kondo","submitted_at":"2025-08-16T01:50:33Z","abstract_excerpt":"We consider the Cauchy problem for derivative fractional Schr\\\"odinger equations (fNLS) on the torus $\\mathbb T$. Recently, the second and third authors established a necessary and sufficient condition on the nonlinearity for well-posedness of semi-linear Schr\\\"odinger equations on $\\mathbb T$. In this paper, we extend this result to derivative fNLS. More precisely, we prove that the necessary and sufficient condition on the nonlinearity is the same as that for semi-linear Schr\\\"odinger equations. However, since we can not employ a gauge transformation for derivative fNLS, we use the modified "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.11866","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/2508.11866/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"}