{"paper":{"title":"Almost Morawetz estimates and global well-posedness for the defocusing $L^2$-critical nonlinear Schr{\\\"o}dinger equation in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benjamin Dodson","submitted_at":"2009-09-23T22:25:47Z","abstract_excerpt":"In this paper, we consider the global well-posedness of the defocusing, $L^{2}$ - critical nonlinear Schr{\\\"o}dinger equation in dimensions $n \\geq 3$. Using the I-method, we show the problem is globally well-posed in $n = 3$ when $s > {2/5}$, and when $n \\geq 4$, for $s > \\frac{n - 2}{n}$. We combine energy increments for the I-method, interaction Morawetz estimates, and almost Morawetz estimates to prove the result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4332","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0909.4332/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"}