{"paper":{"title":"The Cauchy problem for the Ostrovsky equation with positive dispersion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianhua Huang, Jinqiao Duan, Wei Yan, Yongsheng Li","submitted_at":"2015-05-22T09:04:10Z","abstract_excerpt":"This paper is devoted to studying the Cauchy problem for the Ostrovsky equation \\begin{eqnarray*}\n  \\partial_{x}\\left(u_{t}-\\beta \\partial_{x}^{3}u\n  +\\frac{1}{2}\\partial_{x}(u^{2})\\right)\n  -\\gamma u=0, \\end{eqnarray*} with positive $\\beta$ and $\\gamma $. This equation describes the propagation of surface waves in a rotating oceanic flow. We first prove that the problem is locally well-posed in $H^{-\\frac{3}{4}}(\\R)$. Then we reestablish the bilinear estimate, by means of the Strichartz estimates instead of calculus inequalities and Cauchy-Schwartz inequalities. As a byproduct, this bilinear "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05995","kind":"arxiv","version":3},"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"}