{"paper":{"title":"Solvability of the Initial-Boundary value problem of the Navier-Stokes equations with rough 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":"2015-03-30T11:10:39Z","abstract_excerpt":"In this paper, we study the initial and boundary value problem of the Navier-Stokes equations in the half space. We prove the unique existence of weak solution $u\\in L^q(\\R_+\\times (0,T))$ with $\\nabla u\\in L^{\\frac{q}{2}}_{loc}(\\R_+\\times (0,T))$ for a short time interval when the initial data $h\\in {B}_q^{-\\frac{2}{q}}(\\R_+)$ and the boundary data $ g\\in L^q(0,T;B^{-\\frac{1}{q}}_q(\\Rn))+L^q(\\Rn;B^{-\\frac{1}{2q}}_q(0,T)) $ with normal component $g_n\\in L^q(0,T;\\dot{B}^{-\\frac{1}{q}}_q(\\Rn))$, $n+2<q<\\infty$ are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08638","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"}