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arXiv · 1508.00235

Global strong solution to the two-dimensional density-dependent nematic liquid crystal flows with vacuum

Lin Li·Qiao Liu·Xin Zhong
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Abstract

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 $\|\sqrt{ρ_0}\mathbf{u}_0\|_{L^2}^2+\|\nabla\mathbf{d}_0\|_{L^2}^2$ is small. In particular, the initial density may contain vacuum states and even have compact support. Moreover, the large time behavior of the solution is also obtained.

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Lin Li, Qiao Liu, Xin Zhong. 2017-08-07. Global strong solution to the two-dimensional density-dependent nematic liquid crystal flows with vacuum. https://arxiv.org/abs/1508.00235

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