In this paper, we establish the global existence of a suitable weak solution to the co-rotational Beris-Edwards $Q$-tensor system modeling the hydrodynamic motion of nematic liquid crystals with either Landau-De Gennes bulk potential in $\mathbb R^3$ or Ball-Majumdar bulk potential in $\mathbb{T}^3$, a system coupling the forced incompressible Navier-Stokes equation with a dissipative, parabolic system of Q-tensor $Q$ in $\mathbb R^3$, which is shown to be smooth away from a closed set $\Sigma$ whose $1$-dimensional parabolic Hausdorff measure is zero.

中文翻译：

---

三维共转Beris-Edwards系统的合适弱解

在本文中，我们建立了对同向旋转 Beris-Edwards $Q$-张量系统的合适弱解的全局存在性，该系统对向列液晶的流体动力学运动进行建模，其中任一 Landau-De Gennes 体势在 $\mathbb R^ 3$ 或 $\mathbb{T}^3$ 中的 Ball-Majumdar 体势，该系统将受迫不可压缩的 Navier-Stokes 方程与耗散的抛物线系统 Q-张量 $Q$ 耦合在 $\mathbb R^3$ ，它被证明是平滑远离闭集 $\Sigma$，其 $1$ 维抛物线 Hausdorff 测度为零。