{"paper":{"title":"Stable blow-up on a sphere for a quadratic-derivative nonlinear wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Manuel del Pino, Monica Musso, Oliver Gough","submitted_at":"2026-06-21T00:16:29Z","abstract_excerpt":"We study finite-time blow-up for the nonlinear wave equation \\begin{equation*} v_{tt}-\\Delta v=|\\nabla_x v|^2 \\end{equation*} in dimensions $n\\geq2$, under radial symmetry. For every prescribed radius $r_0>0$, we construct solutions which blow up in finite time $T>0$ on the sphere $\\{|x|=r_0\\}$ with logarithmic Type-I rate. The leading singular dynamics are governed by ``generalised self-similar'' profiles of the associated one-dimensional equation, while the radial geometry generates a curvature correction of size $\\mathcal{O}((\\frac{T}{r_0})^2)$. A key simplification in our approach is a log"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22282","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22282/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}