{"paper":{"title":"Local and global well-posedness results for the Benjamin-Ono-Zakharov-Kuznetsov equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francis Ribaud (LAMA), St\\'ephane Vento (LAGA)","submitted_at":"2016-01-05T15:18:26Z","abstract_excerpt":"We show that the initial value problem associated to the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation$$ u\\_t-D\\_x^\\alpha u\\_{x} + u\\_{xyy} = uu\\_x,\\quad (t,x,y)\\in\\R^3,\\quad 1\\le \\alpha\\le 2,$$is locally well-posed in the spaces $E^s$, $s\\textgreater{}\\frac 2\\alpha-\\frac 34$, endowed with the norm$\\|f\\|\\_{E^s} = \\|\\langle |\\xi|^\\alpha+\\mu^2\\rangle^s\\hat{f}\\|\\_{L^2(\\R^2)}.$As a consequence, we get the global well-posedness in the energy space $E^{1/2}$ as soon as $\\alpha\\textgreater{}\\frac 85$. The proof is based on the approach of the short time Bourgain spaces developed by "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00856","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"}