{"paper":{"title":"Sharp asymptotics for the minimal mass blow up solution of critical gKdV equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Vianney Combet, Yvan Martel","submitted_at":"2016-02-10T20:59:34Z","abstract_excerpt":"Let $S$ be a minimal mass blow up solution of the critical generalized KdV equation as constructed by Martel, Merle and Rapha\\\"el in arXiv:1204.4624. We prove both time and space sharp asymptotics for $S$ close to the blow up time. Let $Q$ be the unique ground state of (gKdV), satisfying $Q\"+Q^5=Q$.\n  First, we show that there exist universal smooth profiles $Q_k\\in\\mathcal{S}(\\mathbb{R})$ (with $Q_0=Q$) and a constant $c_0\\in\\mathbb{R}$ such that, fixing the blow up time at $t=0$ and appropriate scaling and translation parameters, $S$ satisfies, for any $m\\geqslant 0$, \\[ \\partial_x^m S(t) - "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03519","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"}