{"paper":{"title":"New $\\varepsilon$-regularity criteria of suitable weak solutions of the 3D Navier-Stokes equations at one scale","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cheng He, Daoguo Zhou, Yanqing Wang","submitted_at":"2017-09-05T13:45:17Z","abstract_excerpt":"In this paper, by invoking the appropriate decomposition of pressure to exploit the energy hidden in pressure, we present some new $\\varepsilon$-regularity criteria for suitable weak solutions of the 3D Navier-Stokes equations at one scale: for any $p,q\\in [1,\\infty]$ satisfying $1\\leq 2/q+3/p <2$, there exists an absolute positive constant $\\varepsilon$ such that $u\\in L^{\\infty}(Q(1/2))$ if\n  $$\\|u\\|_{L^{p,q}(Q(1))}+\\|\\Pi\\|_{L^{1 }(Q(1))}<\\varepsilon.$$ This is an improvement of corresponding results recently proved by Guevara and Phuc in [7, Calc. Var. 56:68, 2017]. As an application of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01382","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"}