{"paper":{"title":"A note on the Ostrovsky 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 Urrea","submitted_at":"2016-03-02T16:37:36Z","abstract_excerpt":"In this work we consider the initial value problem (IVP) associated to the Ostrovsky equations $$\\left. \\begin{array}{rl} u_t+\\partial_x^3 u\\pm \\partial_x^{-1}u +u \\partial_x u &\\hspace{-2mm}=0,\\qquad\\qquad x\\in\\mathbb R,\\; t\\in\\mathbb R,\\\\ u(x,0)&\\hspace{-2mm}=u_0(x). \\end{array} \\right\\}$$ We study the well-posedness of the IVP in the weighted Sobolev spaces $$Z_{s,\\frac{s}2}:=\\{u\\in H^s(\\mathbb R):D_x^{-s} u\\in L^2(\\mathbb R)\\}\\cap L^2(|x|^s dx ),$$ with $\\frac34<s\\leq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00783","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"}