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

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.

44 pages

References in corpus (1)

• Introduction to Q-tensor theory

Cited by in corpus (1)

• On a molecular based Q-tensor model for liquid crystals with density variations