Strong solutions to the density-dependent incompressible nematic liquid crystal flows
Strong solutions to the density-dependent incompressible nematic liquid crystal flows
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密度相关不可压缩向列液晶流的强解
DOI：
10.1016/j.jde.2015.10.047
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发表时间：
2016
影响因子：
2.4
通讯作者：
Yao Zheng-an
中科院分区：
文献类型：
--
作者：
Gao Jincheng;Tao Qiang;Yao Zheng-an
本文研究了一维有界区域中密度相关的不可压缩液晶流动。更精确地说，当流体的粘性系数依赖于密度时，我们得到了解的局部存在唯一性。此外，我们还分别建立了二维和三维强解正则性的爆破准则。特别地，当初始方向场满足某种几何构型时，我们建立了一个仅用密度梯度表示的爆破准则。对于这些结果，初始密度不需要严格为正。
In this paper, we investigate the density-dependent incompressible nematic liquid crystal flows inordimensional 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.