{"paper":{"title":"Well-posedness for the fifth-order KdV equation in the energy space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos E. Kenig, Didier Pilod","submitted_at":"2012-05-01T14:22:10Z","abstract_excerpt":"We prove that the initial value problem (IVP) associated to the fifth order KdV equation {equation} \\label{05KdV} \\partial_tu-\\alpha\\partial^5_x u=c_1\\partial_xu\\partial_x^2u+c_2\\partial_x(u\\partial_x^2u)+c_3\\partial_x(u^3), {equation} where $x \\in \\mathbb R$, $t \\in \\mathbb R$, $u=u(x,t)$ is a real-valued function and $\\alpha, \\ c_1, \\ c_2, \\ c_3$ are real constants with $\\alpha \\neq 0$, is locally well-posed in $H^s(\\mathbb R)$ for $s \\ge 2$. In the Hamiltonian case (\\textit i.e. when $c_1=c_2$), the IVP associated to \\eqref{05KdV} is then globally well-posed in the energy space $H^2(\\mathbb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0169","kind":"arxiv","version":3},"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"}