{"paper":{"title":"Local and global well-posedness for the 2D generalized Zakharov-Kuznetsov equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ademir Pastor, Felipe Linares","submitted_at":"2010-10-26T14:14:28Z","abstract_excerpt":"This paper addresses well-posedness issues for the initial value problem (IVP) associated with the generalized Zakharov-Kuznetsov equation, namely, \\{equation*} \\quad \\left\\{\\{array}{lll} {\\displaystyle u_t+\\partial_x \\Delta u+u^ku_x = 0,}\\qquad (x,y) \\in \\mathbb{R}^2, \\,\\,\\,\\, t>0, {\\displaystyle u(x,y,0)=u_0(x,y)}. \\{array} \\right. \\{equation*} For $2\\leq k \\leq 7$, the IVP above is shown to be locally well-posed for data in $H^s(\\mathbb{R}^2)$, $s>3/4$. For $k\\geq8$, local well-posedness is shown to hold for data in $H^s(\\mathbb{R}^2)$, $s>s_k$, where $s_k=1-3/(2k-4)$. Furthermore, for $k\\g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5404","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"}