{"paper":{"title":"Blow-Up for Nonlinear Wave Equations describing Boson Stars","license":"","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Enno Lenzmann, Juerg Froehlich","submitted_at":"2005-11-01T17:10:07Z","abstract_excerpt":"We consider the nonlinear wave equation $i \\partial_t u= \\sqrt{-\\Delta + m^2} u - (|x|^{-1} \\ast |u|^2) u$ on $\\RR^3$ modelling the dynamics of (pseudo-relativistic) boson stars. For spherically symmetric initial data, $u_0(x) \\in C^\\infty_{\\mathrm{c}}(\\RR^3)$, with negative energy, we prove blow-up of $u(t,x)$ in $H^{1/2}$-norm within a finite time. Physically, this phenomenon describes the onset of \"gravitational collapse\" of a boson star. We also study blow-up in external, spherically symmetric potentials and we consider more general Hartree-type nonlinearities. As an application, we exhibi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0511003","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"}