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Blow up criterion for compressible nematic liquid crystal flows in dimension three. (English) Zbl 1314.76010
Summary: 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.

MSC:
76A15 Liquid crystals
35Q35 PDEs in connection with fluid mechanics
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