{"paper":{"title":"Sharp well-posedness and ill-posedness of the Cauchy problem for the higher-order KdV","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianhua Huang, Minjie Jiang, Wei Yan, Yongsheng Li","submitted_at":"2015-11-08T02:59:02Z","abstract_excerpt":"In this paper, we investigate the Cauchy problem for the higher-order KdV-type equation \\begin{eqnarray*}\n  u_{t}+(-1)^{j+1}\\partial_{x}^{2j+1}u\n  + \\frac{1}{2}\\partial_{x}(u^{2})\n  = 0,j\\in N^{+},x\\in\\mathbf{T}= [0,2\\pi \\lambda) \\end{eqnarray*} with low regularity data and $\\lambda\\geq 1$. Firstly, we show that the Cauchy problem for the periodic higher-order KdV equation is locally well-posed in $H^{s}(\\mathbf{T})$ with $s\\geq -j+\\frac{1}{2},j\\geq2.$ By using some new Strichartz estimate and some new function spaces, we also show that the Cauchy problem for the periodic higher-order KdV equa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02430","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"}