TY - JOUR
T1 - Regularity and Existence of Global Solutions to the Ericksen-Leslie System in ℝ2
AU - Huang, Jinrui
AU - Lin, Fanghua
AU - Wang, Changyou
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2014/10
Y1 - 2014/10
N2 - In this paper, we first establish the regularity theorem for suitable weak solutions to the Ericksen-Leslie system in ℝ2. Building on such a regularity, we then establish the existence of a global weak solution to the Ericksen-Leslie system in ℝ2 for any initial data in the energy space, under the physical constraints on the Leslie coefficients ensuring the dissipation of energy of the system, which is smooth away from at most finitely many times. This extends earlier works by Lin et al. (Arch Ration Mech Anal 197:297-336, 2010) on a simplified nematic liquid crystal flow to the general Ericksen-Leslie system.
AB - In this paper, we first establish the regularity theorem for suitable weak solutions to the Ericksen-Leslie system in ℝ2. Building on such a regularity, we then establish the existence of a global weak solution to the Ericksen-Leslie system in ℝ2 for any initial data in the energy space, under the physical constraints on the Leslie coefficients ensuring the dissipation of energy of the system, which is smooth away from at most finitely many times. This extends earlier works by Lin et al. (Arch Ration Mech Anal 197:297-336, 2010) on a simplified nematic liquid crystal flow to the general Ericksen-Leslie system.
UR - http://www.scopus.com/inward/record.url?scp=84905108249&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84905108249&partnerID=8YFLogxK
U2 - 10.1007/s00220-014-2079-9
DO - 10.1007/s00220-014-2079-9
M3 - Article
AN - SCOPUS:84905108249
SN - 0010-3616
VL - 331
SP - 805
EP - 850
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 2
ER -