Strictly Physical Global Weak Solutions of a Navier–Stokes Q-tensor System with Singular Potential

We study the existence, regularity and so-called ‘strict physicality’ of global weak solutions of a Beris–Edwards system which is proposed as a model for the incompressible flow of nematic liquid crystal materials. An important contribution to the dynamics comes from a singular potential introduced by John Ball and Apala Majumdar which replaces the commonly employed Landau-de Gennes bulk potential. This is built into our model to ensure that a natural physical constraint on the eigenvalues of the Q-tensor order parameter is respected by the dynamics of this system. Moreover, by a maximum principle argument, we are able to construct global strong solutions in dimension two.