{"paper":{"title":"Sharp one component regularity for Navier-Stokes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bin Han, Dong Li, Na Zhao, Zhen Lei","submitted_at":"2017-08-14T13:44:10Z","abstract_excerpt":"We consider the conditional regularity of mild solution $v$ to the incompressible Navier-Stokes equations in three dimensions. Let $e \\in \\mathbb{S}^2$ and $0 < T^\\ast < \\infty$. J. Chemin and P. Zhang \\cite{CP} proved the regularity of $v$ on $(0,T^\\ast]$ if there exists $p \\in (4, 6)$ such that $$\\int_0^{T^\\ast}\\|v\\cdot e\\|^p_{\\dot{H}^{\\frac{1}{2}+\\frac{2}{p}}}dt < \\infty.$$ J. Chemin, P. Zhang and Z. F. Zhang \\cite{CPZ} extended the range of $p$ to $(4, \\infty)$. In this article we settle the case $p \\in [2, 4]$. Our proof also works for the case $p \\in (4,\\infty)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04119","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"}