SIAM Journal on Mathematical Analysis, Volume 53, Issue 3, Page 3123-3157, January 2021.
We consider a magnetic effect on hydrodynamic flows of nematic liquid crystals with unequal elastic constants in dimension two. Under a planar ansatz for the director field and velocity, we derive a reduced Ericksen--Leslie system which consists of a quasilinear parabolic equation and a Navier--Stokes equation involving critical nonlinearity due to elastic anisotropy. When unequal elastic constants are sufficiently close, we establish the global existence of smooth solutions to the reduced system and show convergence to an equilibrium as $t$ tends to $\infty$. A magnetic field-induced instability of the aligned state under the hydrodynamic flow is discussed.

中文翻译：

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外加磁场中各向异性液晶的流体力学

SIAM 数学分析杂志，第 53 卷，第 3 期，第 3123-3157 页，2021 年 1 月。
我们考虑了磁效应对向列液晶的流体动力学流动的影响，在维度 2 中具有不等的弹性常数。在指向场和速度的平面分析下，我们推导出一个简化的 Ericksen-Leslie 系统，它由一个拟线性抛物线方程和一个 Navier-Stokes 方程组成，该方程涉及由于弹性各向异性引起的临界非线性。当不等弹性常数足够接近时，我们建立了简化系统的光滑解的全局存在性，并显示收敛到平衡，因为 $t$ 趋向于 $\infty$。讨论了流体动力流动下对齐状态的磁场引起的不稳定性。