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arXiv · 1810.09961

Global Well-posedness of the Two Dimensional Beris-Edwards System with General Laudau-de Gennes Free Energy

Yuning Liu·Hao Wu·Xiang Xu
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Abstract

In this paper, we consider the Beris-Edwards system for incompressible nematic liquid crystal flows. The system under investigation consists of the Navier-Stokes equations for the fluid velocity $\mathbf{u}$ coupled with an evolution equation for the order parameter $Q$-tensor. One important feature of the system is that its elastic free energy takes a general form and in particular, it contains a cubic term that possibly makes it unbounded from below. In the two dimensional periodic setting, we prove that if the initial $L^\infty$-norm of the $Q$-tensor is properly small, then the system admits a unique global weak solution. The proof is based on the construction of a specific approximating system that preserves the $L^\infty$-norm of the $Q$-tensor along the time evolution.

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Yuning Liu, Hao Wu, Xiang Xu. 2018-10-23. Global Well-posedness of the Two Dimensional Beris-Edwards System with General Laudau-de Gennes Free Energy. https://doi.org/10.1016/j.jde.2019.07.010

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