{"paper":{"title":"On the regularity criteria of weak solutions to the micropolar fluid equations in Lorentz space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baoquan Yuan","submitted_at":"2009-08-05T08:15:57Z","abstract_excerpt":"In this paper the regularity of weak solutions and the blow-up criteria of smooth solutions to the micropolar fluid equations on three dimension space are studied in the Lorentz space $L^{p,\\infty}(\\mathbb{R}^3)$. We obtain that if $u\\in L^q(0,T;L^{p,\\infty}(\\mathbb{R}^3))$ for $\\frac2q+\\frac3p\\le 1$ with $3<p\\le \\infty$; or $\\nabla u\\in L^q(0,T;L^{p,\\infty}(\\mathbb{R}^3))$ for $\\frac2q+\\frac3p\\le 2$ with $\\frac32<p\\le \\infty$; or the pressure $P\\in L^q(0,T;L^{p,\\infty}(\\mathbb{R}^3))$ for $\\frac2q+\\frac3p\\le 2$ with $\\frac32<p\\le \\infty$; or $\\nabla P\\in L^q(0,T;L^{p,\\infty}(\\mathbb{R}^3))$ f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.0614","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"}