{"paper":{"title":"Large global solutions for nonlinear Schr\\\"odinger equations III, energy-supercritical cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Avy Soffer, Marius Beceanu, Qingquan Deng, Yifei Wu","submitted_at":"2019-01-23T03:37:32Z","abstract_excerpt":"In this work, we mainly focus on the energy-supercritical nonlinear Schr\\\"odinger equation, $$\n  i\\partial_{t}u+\\Delta u= \\mu|u|^p u, \\quad (t,x)\\in \\mathbb{R}^{d+1}, $$ with $\\mu=\\pm1$ and $p>\\frac4{d-2}$. %In this work, we consider the energy-supercritical cases, that is, $p\\in (\\frac4{d-2},+\\infty)$.\n  We prove that for radial initial data with high frequency, if it is outgoing (or incoming) and in rough space $H^{s_1}(\\mathbb{R}^d)$ $(s_1<s_c)$ or its Fourier transform belongs to $W^{s_2,1}(\\mathbb{R}^d)$ $(s_2<s_c)$, the corresponding solution is global and scatters forward (or backward) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07709","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"}