{"paper":{"title":"Well-posedness results for the 3D Zakharov-Kuznetsov equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francis Ribaud (LAMA), St\\'ephane Vento (LAGA)","submitted_at":"2011-11-11T20:43:56Z","abstract_excerpt":"We prove the local well-posedness of the three-dimensional Zakharov-Kuznetsov equation $\\partial_tu+\\Delta\\partial_xu+ u\\partial_xu=0$ in the Sobolev spaces $H^s(\\R^3)$, $s>1$, as well as in the Besov space $B^{1,1}_2(\\R^3)$. The proof is based on a sharp maximal function estimate in time-weighted spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2850","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"}