{"paper":{"title":"LPS's Criterion for Incompressible Nematic Liquid Crystal Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guochun Wu, Qing Chen, Zhong Tan","submitted_at":"2012-11-24T16:26:47Z","abstract_excerpt":"In this paper we derive LPS's criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in $\\mathbb R^3$. We show that if $0<T<+\\infty$} is the maximal time interval for the unique smooth solution $u\\in\n  C^\\infty([0,T),\\mathbb\n  R^3)$, then $|u|+|\\nabla d|\\notin L^q([0,T],L^p(\\mathbb\n  R^3))$, where $p$ and $q$ safisfy the Ladyzhenskaya-Prodi-Serrin's condition: $\\frac{3}{p}+\\frac{2}{q}=1$ and $p\\in(3,+\\infty]$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5682","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"}