{"paper":{"title":"On stability of type II blow up for the critical NLW on \\R^{3+1}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joachim Krieger","submitted_at":"2017-05-10T18:15:28Z","abstract_excerpt":"We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation \\[ \\Box u = -u^5 \\] on $\\R^{3+1}$ constructed in earlier work by Krieger-Schlag-Tataru are stable along a co-dimension three manifold of radial data perturbations in a suitable topology, provided the scaling parameter $\\lambda(t) = t^{-1-\\nu}$ is sufficiently close to the self-similar rate, i. e. $\\nu>0$ is sufficiently small. Our method is based on Fourier techniques adapted to time dependent wave operators of the form \\[ -\\partial_t^2 + \\partial_r^2 + \\frac2r\\partial_r +V(\\lambda(t)r) \\] fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03907","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"}