Blow-up Criteria of Strong Solutions to the Ericksen-Leslie System in ℝ3
Blow-up Criteria of Strong Solutions to the Ericksen-Leslie System in ℝ3
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DOI：
10.1080/03605302.2013.871026
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发表时间：
2014-05
影响因子：
1.9
通讯作者：
Min-Chun Hong;Jinkai Li;Z. Xin
中科院分区：
文献类型：
--
作者：
Min-Chun Hong;Jinkai Li;Z. Xin
In this paper, we establish the local well-posedness and blow-up criteria of strong solutions to the Ericksen-Leslie system in ℝ3 for the well-known Oseen-Frank model. The local existence of strong solutions to liquid crystal flows is obtained by using the Ginzburg-Landau approximation approach to guarantee the constraint that the direction vector of the fluid is of length one. We establish four kinds of blow-up criteria, including (i) the Serrin type; (ii) the Beal-Kato-Majda type; (iii) the mixed type, i.e., Serrin type condition for one field and Beal-Kato-Majda type condition on the other one; (iv) a new one, which characterizes the maximal existence time of the strong solutions to the Ericksen-Leslie system in terms of Serrin type norms of the strong solutions to the Ginzburg-Landau approximate system. Furthermore, we also prove that the strong solutions of the Ginzburg-Landau approximate system converge to the strong solution of the Ericksen-Leslie system up to the maximal existence time.
