In  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 Hs 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 Hs 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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics