{"paper":{"title":"Uniqueness criterion of weak solutions for the 3D Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelhafid Younsi (Department of Mathematics, Algeria), Computer Science, University of Djelfa","submitted_at":"2011-04-16T18:41:48Z","abstract_excerpt":"In this paper we establish a new uniqueness result of weak solutions for the 3D Navier-Stokes equations. Under assumption that there is not uniqueness of weak solution in singular time, we prove that if two weak solutions $u$ and $v$ of 3D Navier-Stokes equations belong to $L^{\\frac{5}{2}}\\left( 0,T;V\\right) $ with the same initial datum, then we get $u=v$. In the class $L^{3}\\left( 0,T;V\\right) $, we prove that $u-v\\in$ $C^{0}\\left( 0,T;H\\right) $ and $u=v\\ $when $u_{0}=v_{0}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3255","kind":"arxiv","version":8},"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"}