论文标题
在静态和流体动力学双轴列液晶上
On static and hydrodynamic biaxial nematic liquid crystals
论文作者
论文摘要
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 $(n, m):Ω\to \mathbb S^2\times \mathbb S^2$ with $n\cdot m=0$ in dimension three, and establish that it is smooth off a closed set of $1$-dimension Hausdorff measure 零。在第二部分中，我们将考虑一个简化的Ericksen-Leslie系统，用于双轴域名$（N，M）$在二维域中，并确定存在独特的全球弱解决方案$（u，n，m）$，在任何最初和边界数据的最初和边界数据的最初和边界数据中，它们在最有限的单个单个单个时刻都很平稳。它们扩展到早期结果的双轴神经学，对应于将Hardt-Kindelerherer-lin \ cite {hkl}和通过lin-lin-wang \ cite \ cite {llw10}的单轴液晶的简化流体动力学最小化单轴列表。
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 $(n, m):Ω\to \mathbb S^2\times \mathbb S^2$ 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.
