Abstract
This paper proves the global existence of strong solutions of the 2D liquid crystal model when ν1= k2= 0, ν2= k1= 1 or ν1= k2= 1, ν2= k1= 0. We also prove some regularity criteria when ν1= k1= 1, ν2= k2= 0 or ν1= k1= 0, ν2= k2= 1.
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