Long-Time Behavior of Global Weak Solutions for a Beris-Edwards Type Model of Nematic Liquid Crystals

Abstract

We consider a Beris-Edwards system modeling incompressible liquid crystal flows of nematic type. This system couples a Navier–Stokes system for the fluid velocity with a time-dependent system for the Q-tensor variable, whose spectral decomposition is related to the directors of liquid crystal molecules. The long-time behavior for global weak solutions is studied, proving that each whole trajectory converges to a single equilibrium whenever a regularity hypothesis is satisfied by the energy of the weak solution.