{"paper":{"title":"A priori bound on the velocity in axially symmetric Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Esteban A. Navas, Qi S. Zhang, Zhen Lei","submitted_at":"2013-09-25T19:55:31Z","abstract_excerpt":"Let $v$ be the velocity of Leray-Hopf solutions to the axially symmetric three-dimensional Navier-Stokes equations. Under suitable conditions for initial values, we prove the following a priori bound \\[ |v(x, t)| \\le \\frac{C}{r^2} |\\ln r|^{1/2}, \\]where $r \\in (0, 1/2)$ is the distance from $x$ to the z axis, and $C$ is a constant depending only on the initial value.\n  This provides a pointwise upper bound (worst case scenario) for possible singularities while the recent papers \\cite{CSTY2} and \\cite{KNSS} gave a lower bound. The gap is polynomial order 1 modulo a half log term."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6625","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"}