论文标题
存在用于活性液晶的不均匀DOI模型的全球弱解决方案的存在
Existence of Global Weak Solutions to an Inhomogeneous Doi Model for Active Liquid Crystals
论文作者
论文摘要
在本文中，我们考虑了W. E和P. Zhang [Meth]引入的不均匀DOI模型。应用。肛门，13（2006），第181-198页]。我们将它们的模型扩展到了将Smoluchowski方程式耦合到Navier-Stokes类型方程，以通过引入其他应力张量来进行活动粒子。利用系统的能量和熵结构，我们确定了在被动和活性颗粒的两个和三个空间维度中的全球弱解的存在。特别是，我们的结果对初始数据的最低规律性假设构成，并且对雷诺和黛博拉的数字无限制。
In this paper, we consider an inhomogeneous Doi model which was introduced by W. E and P. Zhang [Meth. Appl. of Anal., 13 (2006), pp. 181 - 198]. We extend their model, which couples a Smoluchowski equation to a Navier-Stokes type equation, for active particles by introducing an additional stress tensor. Exploiting the energetic and entropic structure of the system, we establish the existence of global-in-time weak solutions in two and three space dimensions for both passive and active particles. In particular, our result holds for minimal regularity assumptions on the initial data and without restrictions on the Reynolds and Deborah number.
