Blow Up Criterion for Compressible Nematic Liquid Crystal Flows in Dimension Three

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at a finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of the velocity gradient and the square of the maximum norm of the gradient of a liquid crystal director field.

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