{"paper":{"title":"Global strong solution to the two-dimensional density-dependent nematic liquid crystal flows with vacuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lin Li, Qiao Liu, Xin Zhong","submitted_at":"2015-08-02T13:46:50Z","abstract_excerpt":"We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible nematic liquid crystal flows on the whole space $\\mathbb{R}^{2}$ with vacuum as far field density. It is proved that the 2D nonhomogeneous incompressible nematic liquid crystal flows admits a unique global strong solution provided the initial data density and the gradient of orientation decay not too slow at infinity, and the basic energy $\\|\\sqrt{\\rho_0}\\mathbf{u}_0\\|_{L^2}^2+\\|\\nabla\\mathbf{d}_0\\|_{L^2}^2$ is small. In particular, the initial density may contain vacuum states and even have comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00235","kind":"arxiv","version":2},"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"}