{"paper":{"title":"Local well-posedness for the fifth-order KdV equations on $\\mathbb{T}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chulkwang Kwak","submitted_at":"2015-10-05T02:41:49Z","abstract_excerpt":"This paper is a continuation of the paper \\emph{Low regularity Cauchy problem for the fifth-order modified KdV equations on $\\mathbb{T}$}. In this paper, we consider the fifth-order equation in the Korteweg-de Vries (KdV) hierarchy as following: \\begin{equation*} \\begin{cases} \\partial_t u - \\partial_x^5 u + 30u^2\\partial_x u + 20 u\\partial_x u \\partial_x^3u + 10u \\partial_x^3 u = 0, \\hspace{1em} (t,x) \\in \\mathbb{R} \\times \\mathbb{T}, u(0,x) = u_0(x) \\in H^s(\\mathbb{T}) \\end{cases}. \\end{equation*}\n  We prove the local well-posedness of the fifth-order KdV equation for low regularity Sobolev "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01017","kind":"arxiv","version":2},"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"}