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In this paper we prove the existence of global in time weak solutions for anevolutionary PDE system modelling nonisothermal Landau-de Gennes nematic liquidcrystal (LC) flows in three dimensions of space. In our model, theincompressible Navier-Stokes system for the macroscopic velocity $\vu$ iscoupled to a nonlinear convective parabolic equation describing the evolutionof the Q-tensor $\QQ$, namely a tensor-valued variable representing thenormalized second order moments of the probability distribution function of theLC molecules. The effects of the (absolute) temperature $\vt$ are prescribed inthe form of an energy balance identity complemented with a global entropyproduction inequality. Compared to previous contributions, we can consider herethe physically realistic singular configuration potential $f$ introduced byBall and Majumdar. This potential gives rise to severe mathematicaldifficulties since it introduces, in the Q-tensor equation, a term which is atthe same time singular in $\QQ$ and degenerate in $\vt$. To treat it a carefulanalysis of the properties of $f$, particularly of its blow-up rate, is carriedout.

Nonisothermal nematic liquid crystal flows with the Ball-Majumdar free energy