论文标题
在一种新颖的方法中，用于建模液晶流
On a novel approach for modeling liquid crystalline flows
论文作者
论文摘要
在本文中，我们得出了一个新模型，用于描述液晶流。尽管微观DOI类型模型遭受了基础产品空间的高维度，但更宏观的埃里克森（Ericksen） - 莱斯利类型模型仅描述流量的长时间行为，并且仅在接近平衡附近有效。通过采用能量变异方法，我们得出了一种新的宏观模型，该模型应提供远离平衡的改进描述。我们方法的新颖性在于能量最小化的方式。区分颗粒和流体的速度使我们能够定义能量耗散，而不是在化学势方面，而是在被考虑的速度中差异引起的摩擦方面。我们通过确定新衍生模型的薄弱解决方案来结束这一出版物。
In this paper, we derive a new model for the description of liquid crystalline flows. While microscopic Doi type models suffer from the high dimensionality of the underlying product space, the more macroscopic Ericksen--Leslie type models describe only the long time behavior of the flow and are valid only close to equilibrium. By applying an energetic variational approach, we derive a new macroscopic model which shall provide an improved description far from equilibrium. The novelty of our approach lies in the way the energy is minimized. Distinguishing between the velocities of particles and fluid allows us to define the energy dissipation not in terms of chemical potentials but in terms of friction induced by the discrepancies in the considered velocities. We conclude this publication by establishing the existence of weak solutions to the newly derived model.
