{"paper":{"title":"Optimal polynomial blow up range for critical wave maps","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Can Gao, Joachim Krieger","submitted_at":"2014-03-28T12:16:42Z","abstract_excerpt":"We prove that the critical Wave Maps equation with target $S^2$ and origin $\\mathbb{R}^{2+1}$ admits energy class blow up solutions of the form $$u(t,r)=Q(\\lambda(t)r)+\\epsilon(t,r)$$where $Q: \\mathbb{R}^2 \\to S^2$ is the ground state harmonic map and $\\lambda(t) = t^{-1-\\nu}$ for any $\\nu > 0$. This extends the work [13], where such solutions were constructed under the assumption $\\nu > 1/2$. In light of a result of Struwe [22], our result is optimal for polynomial blow up rates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7356","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"}