{"paper":{"title":"Global in time solvability of the Navier-Stokes equations in the half-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bum Ja Jin, Tongkeun Chang","submitted_at":"2018-09-19T06:40:49Z","abstract_excerpt":"In this paper, we study the initial value problem of the Navier-Stokes equations in the half-space. Let a solenoidal initial velocity be given in the function space $ \\dot{B}_{pq,0}^{\\alpha-\\frac{2}{2}}({\\mathbb R}^n_+)$ for $\\alpha +1 = \\frac{n}p + \\frac2q$ and $0<\\alpha<2$. We prove the global in time existence of weak solution $u\\in L^q(0,\\infty; \\dot B^\\alpha_{pq}({\\mathbb R}^n_+))\\cap L^{q_0}(0, \\infty; L^{p_0}({\\mathbb R}^n_+)) $ for some $ 1<p_0, q_0<\\infty$ with $\\frac{n}{p_0} +\\frac2{q_0} =1$, when the given initial velocity has small norm in function space $ \\dot{B}_{p_0q_0,0}^{-\\fra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07025","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"}