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In this paper, we consider the Cauchy problem of the incompressible liquidcrystal equations in $n$ dimensions. We prove the local well-posedness of mildsolutions to the liquid crystal equations with $L^\infty$ initial data, inparticular, the initial energy may be infinite. We prove that the solutions aresmooth with respect to the space variables away from the initial time. Based onthis regularity estimate, we employ the blow up argument and Liouville typetheorems to establish vorticity direction type blow up criterions for the typeI mild solutions established in the present paper.

Liquid Crystal Equations with Infinite Energy Local Well-posedness and Blow Up Criterion