{"paper":{"title":"Local well-posedness for the $H^2$-critical nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daoyuan Fang, Thierry Cazenave, Zheng Han","submitted_at":"2013-04-20T00:03:59Z","abstract_excerpt":"In this paper, we consider the nonlinear Schr\\\"odinger equation $iu_t +\\Delta u= \\lambda |u|^{\\frac {4} {N-4}} u$ in $\\R^N $, $N\\ge 5$, with $\\lambda \\in \\C$. We prove local well-posedness (local existence, unconditional uniqueness, continuous dependence) in the critical space $\\dot H^2 (\\R^N) $."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5564","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"}