{"paper":{"title":"Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacek Jendrej","submitted_at":"2015-03-17T12:52:46Z","abstract_excerpt":"We consider the semilinear wave equation with focusing energy-critical nonlinearity in space dimension 5 with radial data. It is known that a solution $(u, \\partial_t u)$ which blows up at $t = 0$ in a neighborhood (in the energy norm) of the family of solitons $W_\\lambda$, asymptotically decomposes in the energy space as a sum of a bubble $W_\\lambda$ and an asymptotic profile $(u_0^*, u_1^*)$, where $\\lim_{t\\to 0}\\lambda(t)/t = 0$ and $(u^*_0, u^*_1) \\in \\dot H^1\\times L^2$. We construct a blow-up solution of this type such that $(u^*_0, u^*_1)$ is any pair of sufficiently regular functions w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05024","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"}