{"paper":{"title":"Spatial decay and nonlinear smoothing of the generalized Ostrovsky equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Meihua Yang, Wei Yan, Xiangqian Yan","submitted_at":"2026-05-22T01:45:38Z","abstract_excerpt":"This paper is devoted to studying the generalized Ostrovsky equation \\begin{eqnarray*} u_{t}-\\beta\\partial_{x}^{3}u-\\gamma\\partial_{x}^{-1}u+\\frac{1}{k+1}(u^{k+1})_{x}=0,k\\geq5 \\end{eqnarray*} with $\\beta<0,\\gamma>0$. Firstly, by using the density theorem in the mixed Lebesgue spaces, we prove that $X_{s,b}\\hookrightarrow C(\\mathbb{R};H^{s}(\\mathbb{R})) \\hookrightarrow C(\\mathbb{R};L_{x}^{\\infty})$ with $s>1/2,b>1/2.$ Secondly, we present a new proof of the convergence problem of linear Ostrovsky equation, which is slightly different from the proof of Theorem 1.1 (Convergence problem of Ostrov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23142","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.23142/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}