{"paper":{"title":"On convergence of exterior solutions to radial Cauchy solutions for $\\square_{1+3}U=0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Charis Tsikkou, Helge Kristian Jenssen","submitted_at":"2016-07-22T15:53:16Z","abstract_excerpt":"Consider the Cauchy problem for the 3-d linear wave equation $\\square_{1+3}U=0$ with radial initial data $U(0,x)=\\Phi(x)=\\phi(|x|)$, $U_t(0,x)=\\Psi(x)=\\psi(|x|)$. A standard result gives that $U$ belongs to $C([0,T];H^s(\\mathbb{R}^3))$ whenever $(\\Phi,\\Psi)\\in H^s\\times H^{s-1}(\\mathbb{R}^3)$. In this note we are interested in the question of how $U$ can be realized as a limit of solutions to initial-boundary value problems on the exterior of vanishing balls $B_\\varepsilon$ about the origin. We note that, as the solutions we compare are defined on different domains, the answer is not an immedi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06717","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"}