Blow up criterion for compressible nematic liquid crystal flows in dimension three

Details Blow up criterion for compressible nematic liquid crystal flows in dimension three Blow up criterion for compressible nematic liquid crystal flows in dimension three

2011-04-29

arxiv.org/abs/1104.5685v1

Mathematics

Analysis of PDEs

22 pages

Scientific paper

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

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