Weak compactness of simplified nematic liquid flows in 2D

Hengrong Du; Tao Huang; Changyou Wang

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arXiv · 2006.04210

Weak compactness of simplified nematic liquid flows in 2D

Hengrong Du·Tao Huang·Changyou Wang

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Abstract

For any bounded, smooth domain $\Omega\subset \R^2$, %(or $\Omega=\R^2$), we will establish the weak compactness property of solutions to the simplified Ericksen-Leslie system for both uniaxial and biaxial nematics, and the convergence of weak solutions of the Ginzburg-Landau type nematic liquid crystal flow to a weak solution of the simplified Ericksen-Leslie system as the parameter tends to zero. This is based on the compensated compactness property of the Ericksen stress tensors, which is obtained by the $L^p$-estimate of the Hopf differential for the Ericksen-Leslie system and the Pohozaev type argument for the Ginzburg-Landau type nematic liquid crystal flow.

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Hengrong Du, Tao Huang, Changyou Wang. 2020-06-07. Weak compactness of simplified nematic liquid flows in 2D. https://arxiv.org/abs/2006.04210

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