Nematic liquid crystal under plane oscillatory flows

We consider planarly oriented nematic liquid crystal subjected to plane, rectilinear, oscillatory Couette or Poiseuille flow in the case, when the director is initially perpendicular to the flow plane. Using the Galerkin method we found the critical amplitude of the flow at which the homogeneous instability develops. The analytical approximations for the frequency dependence of the critical amplitude for different types of flow are obtained. The results are compared with experimental data.