{"paper":{"title":"Global well-posedness of partially periodic KP-I equation in the energy space and application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tristan Robert","submitted_at":"2017-06-21T13:43:28Z","abstract_excerpt":"In this article, we address the Cauchy problem for the KP-I equation \\[\\partial_t u + \\partial_x^3 u -\\partial_x^{-1}\\partial_y^2u + u\\partial_x u = 0\\] for functions periodic in $y$. We prove global well-posedness of this problem for any data in the energy space $\\mathbb{E} = \\left\\{u\\in L^2\\left(\\mathbb{R}\\times\\mathbb{T}\\right),~\\partial_x u \\in L^2\\left(\\mathbb{R}\\times\\mathbb{T}\\right),~\\partial_x^{-1}\\partial_y u \\in L^2\\left(\\mathbb{R}\\times\\mathbb{T}\\right)\\right\\}$. We then prove that the KdV line soliton, seen as a special solution of KP-I equation, is orbitally stable under this flo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06903","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"}