A global 2D well-posedness result on the order tensor liquid crystal theory

In [18] Paicu and Zarnescu have studied an order tensor system which describes the flow of a liquid crystal. They have proven the existence of weak solutions, the propagation of higher regularity, namely H^s with s>1 and the weak-strong uniqueness in dimension two. This paper is devoted to fill the gap of their results, namely to propagate the low regularity, namely H^s for 0<s<1 and to prove the uniqueness of the weak solutions. For the completeness of this research, we also propose an alternative approach in order to prove the existence of weak solutions.