{"paper":{"title":"Ill-posedness of the incompressible Navier-Stokes equations in $\\dot{F}^{-1,q}_{\\infty}({R}^3)$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C. Deng, X. Yao","submitted_at":"2013-02-28T05:00:58Z","abstract_excerpt":"In this paper, authors show the ill-posedness of 3D incompressible Navier-Stokes equations in the critical Triebel-Lizorkin spaces $ \\dot{F}^{-1,q}_{\\infty} (\\mathbb{R}^3) $ for any $ q>2 $ in the sense that arbitrarily small initial data of $ \\dot{F}^{-1,q}_{\\infty}(\\mathbb{R}^3) $ can lead the corresponding solution to become arbitrarily large after an arbitrarily short time. In view of the well-posedness of 3D-incompressible Navier-Stokes equations in $ BMO^{-1} $ (i.e. the Triebel-Lizorkin space $ \\dot{F}^{-1,2}_{\\infty}(\\mathbb{R}^3) $) by Koch and Tataru, our work completes a dichotomy o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7084","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"}