Well-posedness of frame hydrodynamics for biaxial nematic liquid crystals

Sirui Li; Chenchen Wang; Jie Xu

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arXiv · 2202.08998

Well-posedness of frame hydrodynamics for biaxial nematic liquid crystals

Sirui Li·Chenchen Wang·Jie Xu

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Abstract

We consider the hydrodynamics for the biaxial nematic phase characterized by a field of orthonormal frame, which can be derived from a molecular-theory-based tensor model. In dimension two and three, we establish the local well-posedness and the blow-up criterion for smooth solutions to the frame hydrodynamic model. Furthermore, we prove the global existence of weak solutions in $\mathbb{R}^2$ which are nonsmooth at finitely many singular times.

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Sirui Li, Chenchen Wang, Jie Xu. 2022-02-18. Well-posedness of frame hydrodynamics for biaxial nematic liquid crystals. https://arxiv.org/abs/2202.08998

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