2015/02/01 by Jincheng Gao, Qiang Tao, Gao, Jincheng +4
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #math.AP
paper · pdf · doi:10.48550/arxiv.1502.00246
46 page. arXiv admin note: text overlap with arXiv:1204.4966, arXiv:1211.0131 by other authors
arxiv created 2015/02/01 · openalex publication_date 2015/02/01 · arxiv updated 2015/02/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we investigate the density-dependent incompressible nematic liquid crystal flows in n(n=2 or 3) dimensional bounded domain. More precisely, we obtain the local existence and uniqueness of the solutions when the viscosity coefficient of fluid depends on density. Moreover, we establish blowup criterions for the regularity of the strong solutions in dimension two and three respectively. In particular, we build a blowup criterion just in terms of the gradient of density if the initial direction field satisfies some geometric configuration. For these results, the initial density needs not be strictly positive.