{"paper":{"title":"Low regularity well-posedness of nonlocal dispersive perturbations of Burgers' equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Didier Pilod, Luc Molinet, St\\'ephane Vento","submitted_at":"2025-06-21T19:59:57Z","abstract_excerpt":"We consider the Cauchy problem associated to a class of dispersive perturbations of Burgers' equations, which contains the low dispersion Benjamin-Ono equation, (also known as low dispersion fractional KdV equation), $$ \\partial_tu-D_x^{\\alpha}\\partial_xu=\\partial_x(u^2) \\, ,$$ and prove that it is locally well-posed in $H^s(\\mathbb K)$, $\\mathbb K=\\mathbb R$ or $\\mathbb T$, for $s>s_{\\alpha}$, where \\begin{equation*} s_\\alpha=\\begin{cases}\n  1-\\frac{3\\alpha}4 & \\text{for} \\quad \\frac23 \\le \\alpha \\le 1;\n  \\frac 32(1-\\alpha) & \\text{for} \\quad \\frac13 \\le \\alpha \\le \\frac23;\n  \\frac 32-\\frac{\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17801","kind":"arxiv","version":2},"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/2506.17801/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"}