{"paper":{"title":"Local and global analyticity for $\\mu$-Camassa-Holm equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hideshi Yamane","submitted_at":"2019-06-27T02:23:56Z","abstract_excerpt":"We solve Cauchy problems for some $\\mu$-Camassa-Holm integro-partial differential equations in the analytic category. The equations to be considered are $\\mu$CH of Khesin-Lenells-Misio\\l{}ek, $\\mu$DP of Lenells-Misio\\l{}ek-Ti\\u{g}lay, the higher-order $\\mu$CH of Wang-Li-Qiao and the non-quasilinear version of Qu-Fu-Liu. We prove the unique local solvability of the Cauchy problems and provide an estimate of the lifespan of the solutions. Moreover, we show the existence of a unique global-in-time analytic solution for $\\mu$CH, $\\mu$DP and the higher-order $\\mu$CH. The present work is the first r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11411","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":""},"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"}