{"paper":{"title":"Blow-Up Dynamics for the $L^2$ critical case of the $2$D Zakharov-Kuznetsov equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francisc Bozgan, Kai Yang, Nader Masmoudi, Tej-Eddine Ghoul","submitted_at":"2024-06-03T15:29:14Z","abstract_excerpt":"We investigate the blow-up dynamics for the $L^2$ critical two-dimensional Zakharov-Kuznetsov equation \\begin{equation*} \\begin{cases} \\partial_t u+\\partial_{x_1} (\\Delta u+u^3)=0, \\mbox{ } x=(x_1,x_2)\\in \\mathbb{R}^2, \\mbox{ } t \\in \\mathbb{R}\\\\ u(0,x_1,x_2)=u_0(x_1,x_2)\\in H^1(\\mathbb{R}^2), \\end{cases} \\end{equation*} with initial data $u_0$ slightly exceeding the mass of the ground state $Q$. Employing methodologies analogous to the Martel-Merle-Raphael blow-up theory for $L^2$ critical equations, more precisely for the critical NLS equation and the quintic generalized Korteweg-de Vries eq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.06568","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/2406.06568/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"}