On asymptotic isotropy for a hydrodynamic model of liquid crystals

Abstract

We study a PDE system describing the motion of liquid crystals by means of the $Q-$tensor description for the crystals coupled with the incompressible Navier-Stokes system. Using the method of Fourier splitting, we show that solutions of the system tend to the isotropic state at the rate $(1+t{)}^{-3/2}$ as $t\to \infty$.