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We study the existence, regularity and so-called `strict physicality' of weaksolutions of a coupled Navier-Stokes Q-tensor system which is proposed as amodel for the incompressible flow of nematic liquid crystal materials. Animportant contribution to the dynamics comes from a singular potentialintroduced by John Ball and Apala Majumdar (Nematic Liquid Crystals: FromMaier-Saupe to a Continuum Theory, Mol. Cryst. Liq. Cryst., Vol. 525: pp. 1-11,2010) which replaces the commonly employed Landau-de Gennes bulk potential.This is built into our model to ensure that a natural physical constraint onthe eigenvalues of the Q-tensor order parameter is respected by the dynamics ofthe system.

Strict Physicality of Global Weak Solutions of a Navier-Stokes Q-tensor System with Singular Potential