{"paper":{"title":"On the Cauchy problem for the periodic fifth-order KP-I equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tristan Robert","submitted_at":"2017-12-04T15:03:43Z","abstract_excerpt":"The aim of this paper is to investigate the Cauchy problem for the periodic fifth order KP-I equation \\[\\partial_t u - \\partial_x^5 u -\\partial_x^{-1}\\partial_y^2u + u\\partial_x u = 0,~(t,x,y)\\in\\mathbb{R}\\times\\mathbb{T}^2\\] We prove global well-posedness for constant $x$ mean value initial data in the space $\\mathbb{E} = \\{u\\in L^2,~\\partial_x^2 u \\in L^2,~\\partial_x^{-1}\\partial_y u \\in L^2\\}$ which is the natural energy space associated with this equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01134","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"}