{"paper":{"title":"Estimates on fractional higher derivatives of weak solutions for the Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexis F. Vasseur, Kyudong Choi","submitted_at":"2011-05-08T15:03:54Z","abstract_excerpt":"We study weak solutions of the 3D Navier-Stokes equations in whole space with $L^2$ initial data. It will be proved that $\\nabla^\\alpha u $ is locally integrable in space-time for any real $\\alpha$ such that $1< \\alpha <3$, which says that almost third derivative is locally integrable. Up to now, only second derivative $\\nabla^2 u$ has been known to be locally integrable by standard parabolic regularization. We also present sharp estimates of those quantities in weak-$L_{loc}^{4/(\\alpha+1)}$. These estimates depend only on the $L^2$ norm of initial data and integrating domains. Moreover, they "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1526","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"}