{"paper":{"title":"Remarks on the global large solution to the three-dimensional incompressible Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jinlu Li, Yanghai Yu, Zhaoyang Yin","submitted_at":"2019-04-03T05:45:29Z","abstract_excerpt":"In this paper, we derive a new smallness hypothesis of initial data for the three-dimensional incompressible Navier-Stokes equations. That is, we prove that there exist two positive constants $c_0,C_0$ such that if \\begin{equation*}\n  \\|u_0^1+u^2_0,u^3_0\\|_{\\dot{B}_{p,1}^{-1+\\frac{3}{p}}} \\|u^1_0,u^2_0\\|_{\\dot{B}_{p,1}^{-1+\\frac{3}{p}}} \\exp\\{C_0 (\\|u_0\\|^{2}_{\\dot{B}_{\\infty,2}^{-1}}+\\|u_0\\|_{\\dot{B}_{\\infty,1}^{-1}})\\} \\leq c_0, \\end{equation*} then \\eqref{NS} has a unique global solution. As an application we construct two family of smooth solutions to the Navier-Stokes equations whose $\\B^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.01779","kind":"arxiv","version":3},"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"}