On the General Ericksen–Leslie System: Parodi’s Relation, Well-Posedness and Stability
On the General Ericksen–Leslie System: Parodi’s Relation, Well-Posedness and Stability
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DOI：
10.1007/s00205-012-0588-2
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发表时间：
2012-11
影响因子：
2.5
通讯作者：
Hao Wu;Xiang Xu;Ryan Chun-Fu Liu
中科院分区：
文献类型：
--
作者：
Hao Wu;Xiang Xu;Ryan Chun-Fu Liu
本文研究了Parodi关系在模拟向列液晶流动的一般Ericksen-Leslie系统的适定性和稳定性中的作用。首先，在Parodi关系下，我们通过适当的能量变分方法给出了Ericksen-Leslie系统的形式化物理推导，其中我们可以区分出诱导弹性应力的保守/耗散部分。其次，在粘度μ4足够大的假设下，证明了Ericksen-Leslie系统的全局适定性和长时性。最后，在Parodi关系下，给出了Ericksen-Leslie系统在局部能量极小点附近的全局适定性和Lyapunov稳定性。讨论了Parodi关系与Ericksen-Leslie系统线性稳定性的关系。
In this paper we investigate the role of Parodi’s relation in the well-posedness and stability of the general Ericksen–Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen–Leslie system through an appropriate energy variational approach under Parodi’s relation, in which we can distinguish the conservative/dissipative parts of the induced elastic stress. Next, we prove global well-posedness and long-time behavior of the Ericksen–Leslie system under the assumption that the viscosityμ4is sufficiently large. Finally, under Parodi’s relation, we show the global well-posedness and Lyapunov stability for the Ericksen–Leslie system near local energy minimizers. The connection between Parodi’s relation and linear stability of the Ericksen–Leslie system is also discussed.