{"paper":{"title":"A solution to the focusing 3d NLS that blows up on a contracting sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Galina Perelman, Justin Holmer, Svetlana Roudenko","submitted_at":"2012-12-26T19:44:04Z","abstract_excerpt":"We rigorously construct radial $H^1$ solutions to the 3d cubic focusing NLS equation $i\\partial_t \\psi + \\Delta \\psi + 2 |\\psi|^2\\psi=0$ that blow-up along a contracting sphere. With blow-up time set to $t=0$, the solutions concentrate on a sphere at radius $\\sim t^{1/3}$ but focus towards this sphere at the faster rate $\\sim t^{2/3}$. Such dynamics were originally proposed heuristically by Degtyarev-Zakharov-Rudakov (1975) and independently later in Holmer-Roudenko (2007), where it was demonstrated to be consistent with all conservation laws of this equation. In the latter paper, it was propo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6236","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"}