{"paper":{"title":"Nonscattering solutions to the $L^{2}$-supercritical NLS Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qing Guo","submitted_at":"2011-01-12T04:44:48Z","abstract_excerpt":"We investigate the nonlinear Schr\\\"{o}dinger equation $iu_{t}+\\Delta u+|u|^{p-1}u=0$ with $1+\\frac{4}{N}<p<1+\\frac{4}{N-2}$ (when $N=1, 2$, $1+\\frac{4}{N}<p<\\infty$) in energy space $H^1$ and study the divergent property of infinite-variance and nonradial solutions. If $M(u)^{\\frac{1-s_{c}}{s_{c}}}E(u)<M(Q)^{\\frac{1-s_{c}}{s_{c}}}E(Q)$ and $\\|u_{0}\\|_{2}^{\\frac{1-s_{c}}{s_{c}}}\\|\\nabla u_{0}\\|_{2}>\\|Q\\|_{2}^{\\frac{1-s_{c}}{s_{c}}}\\|\\nabla Q\\|_{2},$ then either $u(t)$~blows up in finite forward time, or $u(t)$ exists globally for positive time and there exists a time sequence $t_{n}\\rightarrow+"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2271","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"}