{"paper":{"title":"A regularity criterion for three-dimensional micropolar fluid equations in Besov spaces of negative regular indices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fan Wu, Maria Alessandra Ragusa","submitted_at":"2020-05-31T13:46:44Z","abstract_excerpt":"In this article, we study regularity criteria for the 3D micropolar fluid equations in terms of one partial derivative of the velocity. It is proved that if \\begin{equation*} \\int^{T}_{0}\\|\\partial_{3}u\\|^{\\frac{2}{1-r}}_{\\dot{B}^{-r}_{\\infty,\\infty}} dt<\\infty \\quad \\text{with} \\quad 0< r<1, \\end{equation*} then, the solutions of the micropolar fluid equations actually are smooth on $(0, T)$. This improves and extends many previous results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.00524","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.00524/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}