{"paper":{"title":"Critical one component anisotropic regularity for 3-D Navier-Stokes system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ping Zhang, Yanlin Liu","submitted_at":"2017-12-25T14:25:20Z","abstract_excerpt":"Let us consider an initial data $v_0$ for the classical 3D Navier-Stokes equation with vorticity belonging to $L^{\\frac 32}\\cap L^2$.\n  We prove that if the solution associated with $v_0$ blows up at a finite time $T^\\star$, then for any $p\\in]4,\\infty[,~q_1\\in[1,2[,~\\mu>0, ~q_2\\in\\bigl[2,\\bigl(1/p+\\mu\\bigr)^{-1}\\bigr[,~\\kappa\\in ]1,\\infty[$, and any unit vector $e$, the $L^p$ estimate in time of $\\bigl\\|(v(t)|e)_{\\mathbb{R}^3}\\bigr\\|_{L^{\\frac{3p}{p-2}}}^p +\\bigl\\|(v(t)|e)_{\\mathbb{R}^3}\\bigr\\|^p_{ \\bigl(\\dot{B}^{\\mu+\\frac2p+\\frac2{q_1}-1}_{q_1,\\kappa}\\bigr)_{\\rm h} \\bigl(\\dot{B}^{\\frac1{q_2}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09072","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"}