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

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• 作者：Francesco De Anna ^{Francesco.Deanna@math.u-bordeaux1.fr}
• 关键词：76A15 ; 35Q30 ; 35Q35 ; 76D03
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 April 2017
• 年：2017
• 卷：262
• 期：7
• 页码：3932-3979
• 全文大小：541 K
• 卷排序：262

文摘

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 HsHs with s>1s>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 HsHs for 0<s<10<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.