{"paper":{"title":"The Zakharov-Kuznetsov equation in weighted Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eddye Bustamante, Jorge Mej\\'ia, Jos\\'e Jim\\'enez","submitted_at":"2014-12-09T23:23:07Z","abstract_excerpt":"In this work we consider the initial value problem (IVP) associated to the two dimensional Zakharov-Kuznetsov equation $$\\left. \\begin{array}{rl} u_t+\\partial_x^3 u+\\partial_x \\partial_y^2 u +u \\partial_x u &\\hspace{-2mm}=0,\\qquad\\qquad (x,y)\\in\\mathbb R^2,\\; t\\in\\mathbb R,\\\\ u(x,y,0)&\\hspace{-2mm}=u_0(x,y). \\end{array} \\right\\}$$ We study the well-posedness of the IVP in the weighted Sobolev spaces $$H^s(\\mathbb R^2) \\cap L^2((1+x^2+y^2)^{r} dx dy),$$ with $s,r\\in\\mathbb R$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3155","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"}