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arXiv · 1410.3286

Local well-posedness and small Deborah limit of a molecule-based $Q$-tensor system

Sirui Li·Wei Wang·Pingwen Zhang
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Abstract

In this paper, we consider a hydrodynamic $Q$-tensor system for nematic liquid crystal flow, which is derived from Doi-Onsager molecular theory by the Bingham closure. We first prove the existence and uniqueness of local strong solution. Furthermore, by taking Deborah number goes to zero and using the Hilbert expansion method, we present a rigorous derivation from the molecule-based $Q$-tensor theory to the Ericksen-Leslie theory.

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Sirui Li, Wei Wang, Pingwen Zhang. 2014-10-13. Local well-posedness and small Deborah limit of a molecule-based $Q$-tensor system. https://arxiv.org/abs/1410.3286

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