We study an initial boundary value problem of two-dimensional (2D) inhomogeneous incompressible nematic liquid crystal flows with nonnegative density. It is proved that there exists a unique global strong solution provided that the initial orientation satisfies a geometric condition.

中文翻译：

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二维非均匀向列液晶在有界域中流动的全局强解注记

我们研究了具有非负密度的二维 (2D) 非均匀不可压缩向列液晶流的初始边界值问题。证明了当初始方向满足几何条件时，存在唯一的全局强解。