{"paper":{"title":"On the critical one component regularity for 3-D Navier-Stokes system: general case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean-Yves Chemin, Ping Zhang, Zhifei Zhang","submitted_at":"2015-09-07T09:03:23Z","abstract_excerpt":"Let us consider an initial data $v_0$ for the homogeneous incompressible 3D Navier-Stokes equation with vorticity belonging to $L^{\\frac 32}\\cap L^2$. We prove that if the solution associated with $v_0$ blows up at a finite time $T^\\star$, then for any $p$ in $]4,\\infty[$, and any unit vector $e$ of $\\R^3$, the $L^p$ norm in time with value in $\\dot{H}^{\\frac 12+\\frac 2 p }$ of $(v|e)_{\\R^3}$ blows up at $T^\\star$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01952","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"}