TY - JOUR
T1 - Global Existence of Weak Solutions of the Nematic Liquid Crystal Flow in Dimension Three
AU - Lin, Fanghua
AU - Wang, Changyou
N1 - Publisher Copyright:
© 2016 Wiley Periodicals, Inc.
PY - 2016/8/1
Y1 - 2016/8/1
N2 - For any bounded smooth domain Ω ⊂ ℝ3 (or Ω = ℝ3), we establish the global existence of a weak solution (u, d) : Ω × [0, +∞) → ℝ3 × S2 of the initial boundary value (or the Cauchy) problem of the simplified Ericksen-Leslie system (1.1) modeling the hydrodynamic flow of nematic liquid crystals for any initial and boundary (or Cauchy) data (u0, d0) є H × H1(Ω, S2), with d0(Ω) ⊂ S2 (the upper hemisphere). Furthermore, (u, d) satisfies the global energy inequality (1.4).
AB - For any bounded smooth domain Ω ⊂ ℝ3 (or Ω = ℝ3), we establish the global existence of a weak solution (u, d) : Ω × [0, +∞) → ℝ3 × S2 of the initial boundary value (or the Cauchy) problem of the simplified Ericksen-Leslie system (1.1) modeling the hydrodynamic flow of nematic liquid crystals for any initial and boundary (or Cauchy) data (u0, d0) є H × H1(Ω, S2), with d0(Ω) ⊂ S2 (the upper hemisphere). Furthermore, (u, d) satisfies the global energy inequality (1.4).
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U2 - 10.1002/cpa.21583
DO - 10.1002/cpa.21583
M3 - Article
AN - SCOPUS:84929643188
SN - 0010-3640
VL - 69
SP - 1532
EP - 1571
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 8
ER -