{"paper":{"title":"The Cauchy problem for the Ostrovsky equation with negative dispersion at the critical regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianhua Huang, Wei Yan, Yongsheng Li","submitted_at":"2014-11-04T12:56:00Z","abstract_excerpt":"In this paper, we investigate 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*} in the Sobolev space $H^{-3/4}(\\R)$. Here $\\beta>0(<0)$ corresponds to the positive (negative) dispersion of the media, respectively. P. Isaza and J. Mej\\'{\\i}a (J. Diff. Eqns. 230(2006), 601-681; Nonli. Anal. 70(2009), 2306-2316), K. Tsugawa (J. Diff. Eqns. 247(2009), 3163-3180) proved that the problem is locally well-posed in $H^s(\\R)$ when $s>-3/4$ and ill-posed when $s<-3/4$. B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0890","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"}