Abstract
This paper is concerned with a simplified hydrodynamic equation, proposed by Ericksen and Leslie, modeling the flow of nematic liquid crystals. In dimension two, we establish both interior and boundary regularity theorems for such a flow under smallness conditions. As a consequence, we establish the existence of global (in time) weak solutions on a bounded smooth domain in \({\mathbb{R}^2}\) which are smooth everywhere with possible exceptions of finitely many singular times.
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Communicated by J. Ball and R. James
Fanghua Lin and Changyou Wang are partially supported by NSF.
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Lin, F., Lin, J. & Wang, C. Liquid Crystal Flows in Two Dimensions. Arch Rational Mech Anal 197, 297–336 (2010). https://doi.org/10.1007/s00205-009-0278-x
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DOI: https://doi.org/10.1007/s00205-009-0278-x