{"paper":{"title":"A (concentration-)compact attractor for high-dimensional non-linear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Terence Tao","submitted_at":"2006-11-13T20:00:49Z","abstract_excerpt":"We study the asymptotic behavior of large data solutions to Schr\\\"odinger equations $i u_t + \\Delta u = F(u)$ in $\\R^d$, assuming globally bounded $H^1_x(\\R^d)$ norm (i.e. no blowup in the energy space), in high dimensions $d \\geq 5$ and with nonlinearity which is energy-subcritical and mass-supercritical. In the spherically symmetric case, we show that as $t \\to +\\infty$, these solutions split into a radiation term that evolves according to the linear Schr\\\"odinger equation, and a remainder which converges in $H^1_x(\\R^d)$ to a compact attractor, which consists of the union of spherically sym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611402","kind":"arxiv","version":6},"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"}