{"paper":{"title":"Nonscattering solutions and blowup at infinity for the critical wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Joachim Krieger, Roland Donninger","submitted_at":"2012-01-16T14:01:06Z","abstract_excerpt":"We consider the critical focusing wave equation $(-\\partial_t^2+\\Delta)u+u^5=0$ in $\\R^{1+3}$ and prove the existence of energy class solutions which are of the form [u(t,x)=t^\\frac{\\mu}{2}W(t^\\mu x)+\\eta(t,x)] in the forward lightcone ${(t,x)\\in\\R\\times \\R^3: |x|\\leq t, t\\gg 1}$ where $W(x)=(1+(1/3)|x|^2)^{-(1/2)}$ is the ground state soliton, $\\mu$ is an arbitrary prescribed real number (positive or negative) with $|\\mu|\\ll 1$, and the error $\\eta$ satisfies [|\\partial_t \\eta(t,\\cdot)|_{L^2(B_t)} +|\\nabla \\eta(t,\\cdot)|_{L^2(B_t)}\\ll 1,\\quad B_t:={x\\in\\R^3: |x|<t}] for all $t\\gg 1$. Furtherm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3258","kind":"arxiv","version":3},"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"}