{"paper":{"title":"On formation of a locally self-similar collapse in the incompressible Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Dongho Chae, Roman Shvydkoy","submitted_at":"2012-01-29T02:15:14Z","abstract_excerpt":"The paper addresses the question of existence of a locally self-similar blow-up for the incompressible Euler equations. Several exclusion results are proved based on the $L^p$-condition for velocity or vorticity and for a range of scaling exponents. In particular, in $N$ dimensions if in self-similar variables $u \\in L^p$ and $u \\sim \\frac{1}{t^{\\a/(1+\\a)}}$, then the blow-up does not occur provided $\\a >N/2$ or $-1<\\a\\leq N/p$. This includes the $L^3$ case natural for the Navier-Stokes equations. For $\\a = N/2$ we exclude profiles with an asymptotic power bounds of the form $ |y|^{-N-1+\\d} \\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6009","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"}