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Well‐posedness for the density‐dependent incompressible flow of liquid crystals
Author(s) -
Xu Fuyi,
Hao Shengang,
Yuan Jia
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3248
Subject(s) - mathematics , compressibility , besov space , initial value problem , constant (computer programming) , vector field , space (punctuation) , flow (mathematics) , mathematical analysis , cauchy problem , work (physics) , field (mathematics) , incompressible flow , mathematical physics , pure mathematics , geometry , mechanics , physics , interpolation space , thermodynamics , functional analysis , biochemistry , chemistry , linguistics , philosophy , computer science , gene , programming language
In this paper, we are concerned with the Cauchy problem for the density‐dependent incompressible flow of liquid crystals in thewhole space (N ≥ 2).We prove the localwell‐posedness for large initial velocity field and director field of the system in critical Besov spaces if the initial density is close to a positive constant. We show also the global well‐posedness for this system under a smallness assumption on initial data. In particular, this result allows us to work in Besov space with negative regularity indices, where the initial velocity becomes small in the presence of the strong oscillations. Copyright © 2014 John Wiley & Sons, Ltd.