On static and hydrodynamic biaxial nematic liquid crystals [article]

Junyu Lin, Yimei Li, Changyou Wang
2020 arXiv   pre-print
In the first part of this paper, we will consider minimizing configurations of the Oseen-Frank energy functional E(n, m) for a biaxial nematics (n, m):Ω→S^2×S^2 with n· m=0 in dimension three, and establish that it is smooth off a closed set of 1-dimension Hausdorff measure zero. In the second part, we will consider a simplified Ericksen-Leslie system for biaxial nematics (n, m) in a two dimensional domain and establish the existence of a unique global weak solution (u, n, m) that is smooth off
more » ... at most finitely many singular times for any initial and boundary data of finite energy. They extend to biaxial nematics of earlier results corresponding to minimizing uniaxial nematics by Hardt-Kindelerherer-Lin and a simplified hydrodynamics of uniaxial liquid crystal by Lin-Lin-Wang respectively.
arXiv:2006.04207v1 fatcat:pzbmvxvesbd33ex3nq5gzzgy6i