A blow‐up criterion for the compressible nematic liquid crystal flows in three dimensions.

In this paper, we consider the strong solutions under three different types of boundary problems to a compressible nematic liquid crystals system in three dimensions. We establish the blow‐up criterion in terms of the density and the gradient of direction field, provided the shear viscosity and bulk viscosity coefficients of the fluid satisfy an additional relation (i.e., μ>λ$$ \mu >\lambda $$). In particular, the initial vacuum is allowed. [ABSTRACT FROM AUTHOR]