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Abstract:
We study the global existence of weak solutions to a multi-dimensional simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals with large initial energy in a bounded domain Omega subset of R-N, where N = 2 or 3. By exploiting a maximum principle, Nirenberg's interpolation inequality and a smallness condition imposed on the N-th component of initial direction field d(0) to overcome the difficulties induced by the supercritical nonlinearity vertical bar del d vertical bar(2)d in the equations of angular momentum, and then adapting a modified three-dimensional approximation scheme and the weak convergence arguments for the compressible Navier-Stokes equations, we establish the global existence of weak solutions to the initial-boundary problem with large initial energy and without any smallness condition on the initial density and velocity. (C) 2013 Elsevier Inc. All rights reserved.
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Source :
JOURNAL OF FUNCTIONAL ANALYSIS
ISSN: 0022-1236
Year: 2013
Issue: 12
Volume: 265
Page: 3369-3397
1 . 1 5 2
JCR@2013
1 . 7 0 0
JCR@2023
ESI Discipline: MATHEMATICS;
JCR Journal Grade:1
CAS Journal Grade:2
Cited Count:
WoS CC Cited Count: 77
SCOPUS Cited Count: 75
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 1
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