{"paper":{"title":"The IVP for the Benjamin-Ono-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":"Ademir Pastor, Alysson Cunha","submitted_at":"2013-05-02T16:49:23Z","abstract_excerpt":"In this paper we study the initial-value problem associated with the Benjamin-Ono-Zakharov-Kuznetsov equation. We prove that the IVP for such equation is locally well-posed in the usual Sobolev spaces $H^{s}(\\R^2),$ $s>2$, and in the anisotropic spaces $H^{s_1,s_2}(\\R^2)$, $s_2>2$, $s_1\\geq s_2$. We also study the persistence properties of the solution and local well-posedness in the weighted Sobolev class $$ \\mathcal{Z}_{s,r}=H^{s}(\\R^{2})\\cap L^{2}((1+x^{2} +y^{2})^rdxdy), $$ where $s>2$, $r\\geq 0$, and $s\\geq 2r$. Unique continuation properties of the solution are also established. These co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0509","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"}