{"paper":{"title":"Initial-Boundary value problem of the Navier-Stokes equations in the half space with nonhomogeneous data","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":"2018-06-07T05:39:44Z","abstract_excerpt":"This paper discusses the solvability (global in time) of the initial-boundary value problem of the Navier-stokes equations in the half space when the initial data $ h\\in \\dot{ B}_{q \\sigma}^{\\alpha-\\frac{2}{q}}(\\R_+)$ and the boundary data $ g\\in \\dot{ B}_q^{\\alpha-\\frac{1}{q},\\frac{\\al}{2}-\\frac{1}{2q}}({\\mathbb R}^{n-1}\\times {\\mathbb R}_+) $ with $g_n\\in \\dot B^{\\frac12 \\alpha}_q ({\\mathbb R}_+; \\dot B^{-\\frac1q}_q ({\\mathbb R}^{n-1}))\\cap L^q({\\mathbb R}_+;\\dot{B}^{\\alpha-\\frac{1}{q}}(\\Rn))$, for any $0<\\alpha<2$ and $q =\\frac{n+2}{\\alpha+1}$. Compatibility condition is required for $h$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02518","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"}