{"paper":{"title":"The Cauchy problem for a fifth order KdV equation in weighted Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eddye Bustamante, Jorge Mej\\'ia, Jos\\'e Jim\\'enez","submitted_at":"2013-12-05T14:05:19Z","abstract_excerpt":"In this work we study the initial value problem (IVP) for the fifth order KdV equations, \\begin{align*} \\partial_{t}u+\\partial_{x}^{5}u+u^k\\partial_{x}u=0,\\text{} & \\quad x,t\\in \\mathbb R, \\quad k=1,2, \\end{align*} in weighted Sobolev spaces $H^s(\\mathbb R)\\cap L^2(\\langle x \\rangle^{2r}dx)$. We prove local and global results. In the case $k=2$ we point out the relation between decay and regularity of the solution of the IVP."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1552","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"}