Global solution to the nematic liquid crystal flows with heat effect

Dongfen Bian; Yao Xiao

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arXiv · 1604.04082

Global solution to the nematic liquid crystal flows with heat effect

Dongfen Bian·Yao Xiao

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Abstract

The temperature-dependent incompressible nematic liquid crystal flows in a bounded domain $\Omega\subset\mathbb{R}^N$ ($N=2, 3$) are studied in this paper. Following Danchin's method in [J. Math. Fluid Mech., 2006], we use a localization argument to recover the maximal regularity of Stokes equation with variable viscosity, by which we first prove the local existence of strong solution, then extend it to a global one provided that the initial data is a sufficiently small perturbation around the trivial equilibrium state. This paper also generalizes Hu-Wang's result in [Commun. Math. Phys., 2010] to the non-isothermal case.

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Dongfen Bian, Yao Xiao. 2016-04-14. Global solution to the nematic liquid crystal flows with heat effect. https://arxiv.org/abs/1604.04082

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