{"paper":{"title":"Quasilinear normal form for the Kirchhoff-Poho{\\v z}aev equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Emanuele Haus, Simone Marrocco","submitted_at":"2026-07-31T09:57:08Z","abstract_excerpt":"On the $n$-dimensional torus $\\mathbb{T}^n$, we consider the Kirchhoff-Poho{\\v z}aev equation, which is the only Kirchhoff-type equation known to admit global\n  solutions for small initial data in $H^s \\times H^{s-1}$, $s \\geq 2$.\n  We study this equation from a dynamical perspective by means of a quasilinear\n  normal form approach. We perform two steps of normal form reduction and show\n  that the resulting cubic and quintic terms do not contribute to the Sobolev\n  energy estimates. This cancellation reveals a special algebraic structure of the\n  equation and represents a first step towards a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29226","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/2607.29226/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"}