{"paper":{"title":"Global well-posedness and Nonsqueezing property for the higher-order KdV-type flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chulkwang Kwak, Sunghyun Hong","submitted_at":"2015-11-12T08:02:19Z","abstract_excerpt":"In this paper, we prove that the periodic higher-order KdV-type equation \\[\\left\\{\\begin{array}{ll} \\partial_t u + (-1)^{j+1} \\partial_x^{2j+1}u + \\frac12 \\partial_x(u^2)=0, \\hspace{1em} &(t,x) \\in \\mathbb{R} \\times \\mathbb{T}, \\\\ u(0,x) = u_0(x), &u_0 \\in H^s(\\mathbb{T}). \\end{array} \\right.\\] is globally well-posed in $H^s$ for $s \\ge -\\frac{j}{2}$, $j \\ge 3$. The proof of the global well-posedness is based on \"I-method\" introduced by Colliander et al. \\cite{CKSTT1}. To apply \"I-method\", we factorize the resonant functions by using the different ways from Hirayama \\cite{Hirayama}. Furthermor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03808","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"}