{"paper":{"title":"Bilinear Strichartz estimates for the Zakharov-Kuznetsov equation and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Didier Pilod, Luc Molinet","submitted_at":"2013-02-12T21:55:34Z","abstract_excerpt":"This article is concerned with the Zakharov-Kuznetsov equation {equation} \\label{ZK0} \\partial_tu+\\partial_x\\Delta u+u\\partial_xu=0 . {equation} We prove that the associated initial value problem is locally well-posed in $H^s(\\mathbb R^2)$ for $s>\\frac12$ and globally well-posed in $H^1(\\mathbb R\\times \\mathbb T)$ and in $H^s(\\R^3) $ for $ s>1$. Our main new ingredient is a bilinear Strichartz estimate in the context of Bourgain's spaces which allows to control the high-low frequency interactions appearing in the nonlinearity of \\eqref{ZK0}. In the $\\mathbb R^2$ case, we also need to use a rec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2933","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"}