{"paper":{"title":"Blowup for Biharmonic NLS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Enno Lenzmann, Thomas Boulenger","submitted_at":"2015-03-05T19:35:32Z","abstract_excerpt":"We consider the Cauchy problem for the biharmonic (i.\\,e.~fourth-order) NLS with focusing nonlinearity given by $i \\partial_t u = \\Delta^2 u - \\mu \\Delta u -|u|^{2 \\sigma} u$ for $(t,x) \\in [0,T) \\times \\mathbb{R}^d$, where $0 < \\sigma <\\infty$ for $d \\leq 4$ and $0 < \\sigma \\leq 4/(d-4)$ for $d \\geq 5$; and $\\mu \\in \\mathbb{R}$ is some parameter to include a possible lower-order dispersion. In the mass-supercritical case $\\sigma > 4/d$, we prove a general result on finite-time blowup for radial data in $H^2(\\mathbb{R}^d)$ in any dimension $d \\geq 2$. Moreover, we derive a universal upper boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01741","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"}