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arXiv · 1507.06471

Global well-posedness of the 2D nonhomogeneous incompressible nematic liquid crystal flows with vacuum

Qiao Liu·Shengquan Liu·Wenke Tan·Xin Zhong
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Abstract

This paper concerns 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 initial orientation satisfies a geometric condition (see \eqref{eq1.3}). In particular, the initial data can be arbitrarily large and the initial density may contain vacuum states and even have compact support. As a byproduct, the large time behavior of the solution is also obtained.

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Qiao Liu, Shengquan Liu, Wenke Tan, Xin Zhong. 2015-07-23. Global well-posedness of the 2D nonhomogeneous incompressible nematic liquid crystal flows with vacuum. https://arxiv.org/abs/1507.06471

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