TY - JOUR
T1 - On the General Ericksen-Leslie System
T2 - Parodi's Relation, Well-Posedness and Stability
AU - Wu, Hao
AU - Xu, Xiang
AU - Liu, Chun
N1 - Funding Information:
Hao Wu was partially supported by the NSF of China 11001058, Specialized Research Fund for the Doctoral Program of Higher Education and the “Chen Guang” project supported by the Shanghai Municipal Education Commission and the Shanghai Education Development Foundation. Chun Liu and Xiang Xu were partially supported by NSF grants DMS-0707594 and DMS-1109107.
PY - 2013/4
Y1 - 2013/4
N2 - 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 viscosity μ4 is 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.
AB - 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 viscosity μ4 is 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.
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U2 - 10.1007/s00205-012-0588-2
DO - 10.1007/s00205-012-0588-2
M3 - Article
AN - SCOPUS:84874196220
SN - 0003-9527
VL - 208
SP - 59
EP - 107
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 1
ER -