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Paicu and Zarnescu have studied an order tensor system which describes theflow of a liquid crystal. They have proven the existence of weak solutions, thepropagation of higher regularities, namely $H^s$ with $s>1$ and the weak-stronguniqueness in dimension two. This paper is devoted to the propagation of lowerregularities, namely $H^s$ for $0<s\leq 1$ and to prove the uniqueness of theweak solutions. For the completeness of this research, we also propose analternative approach in order to prove the existence of weak solutions.

A Global 2D Well-Posedness Result on the Order Tensor Liquid Crystal Theory