A Global 2D Well-Posedness Result on the Order Tensor Liquid Crystal Theory
Abstract
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 regularities, namely Hs with s>1 and the weak-strong uniqueness in dimension two. This paper is devoted to the propagation of lower regularities, 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.
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