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 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
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
VL - 208
SP - 59
EP - 107
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 1
ER -