Abstract
In this paper, we give a representation formula for the solutions of incompressible liquid crystal flow in arbitrary dimensions. As a direct application, one can obtain a strong global solution in two dimensions, as long as the image of the initial orientation field of the liquid crystal lies in a plane, or is a nontrivial curve on the unit sphere. The results also hold for inhomogeneous incompressible liquid crystals. This generalizes the results in Gong et al (2015 Nonlinearity 28 3677–94) and Dong and Lei (2012 (arXiv:org/abs/1205.3697)).
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