{"paper":{"title":"A Regularity Criterion for Solutions to the 3D NSE in `Dynamically Restricted' Local Morrey Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Liaosha Xu, Zoran Grujic","submitted_at":"2019-03-09T17:40:38Z","abstract_excerpt":"It is shown that a local-in-time strong solution $u$ to the 3D Navier-Stokes equations remains regular on an interval $(0,T)$ provided a smallness $\\epsilon_0$-condition on $u$ in a lower time-restricted local Morrey space is stipulated; more precisely, $$\\sup_{t\\in(0,T)} \\ \\sup_{x \\in \\mathbb{R}^3, \\ \\eta(t) \\le r \\le 1} \\ \\frac{1}{r^\\alpha} \\int_{B_r(x)} |u(y,t)|^p dy \\le \\epsilon_0$$ where $\\eta$ is a dynamic dissipation scale consistent with the turbulence phenomenology and $\\alpha$ and $p$ are suitable parameters. Such regularity criterion guarantees the volumetric sparseness of local spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03833","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"}