{"paper":{"title":"Global well-posedness and limit behavior for a higher-order Benjamin-Ono equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Didier Pilod, Luc Molinet (LMPT)","submitted_at":"2011-11-03T14:43:31Z","abstract_excerpt":"In this paper, we prove that the Cauchy problem associated to the following higher-order Benjamin-Ono equation $$ \\partial_tv-b\\mathcal{H}\\partial^2_xv- a\\epsilon \\partial_x^3v=cv\\partial_xv-d\\epsilon \\partial_x(v\\mathcal{H}\\partial_xv+\\mathcal{H}(v\\partial_xv)), $$ is globally well-posed in the energy space $H^1(\\mathbb R)$. Moreover, we study the limit behavior when the small positive parameter $\\epsilon$ tends to zero and show that, under a condition on the coefficients $a$, $b$, $c$ and $d$, the solution $v_{\\epsilon}$ to this equation converges to the corresponding solution of the Benjami"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0858","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"}