  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 $(n,
m):\Omega\to \mathbb S^2\times \mathbb S^2$ with $n\cdot m=0$ 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 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 \cite{HKL} and a simplified hydrodynamics of uniaxial
liquid crystal by Lin-Lin-Wang \cite{LLW10} respectively.
