Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals

We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law and prove a global well-posedness result. We further provide an example of twist-wave solutions, that is solutions of the coupled system for which the flow vanishes for all times.