{"paper":{"title":"Global well-posedness and scattering for the mass critical nonlinear Schr{\\\"o}dinger equation with mass below the mass of the ground state","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Benjamin Dodson","submitted_at":"2011-04-06T14:40:10Z","abstract_excerpt":"In this paper we prove that the focusing, $d$-dimensional mass critical nonlinear Schr{\\\"o}dinger initial value problem is globally well-posed and scattering for $u_{0} \\in L^{2}(\\mathbf{R}^{d})$, $\\| u_{0} \\|_{L^{2}(\\mathbf{R}^{d})} < \\| Q \\|_{L^{2}(\\mathbf{R}^{d})}$, where $Q$ is the ground state, and $d \\geq 1$. We first establish an interaction Morawetz estimate that is positive definite when $\\| u_{0} \\|_{L^{2}(\\mathbf{R}^{d})} < \\| Q \\|_{L^{2}(\\mathbf{R}^{d})}$, and has the appropriate scaling. Next, we will prove a frequency localized interaction Morawetz estimate similar to the estimat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1114","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":""},"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"}