On decay estimates of the 3D nematic liquid crystal flows in critical Besov spaces |
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Authors: | Qiao Liu Jihong Zhao |
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Institution: | 1. Department of Mathematics, Hunan Normal University, Changsha, Hunan, China;2. College of Science, Northwest A&F University, Yangling, Shaanxi, China |
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Abstract: | In this paper, we develop the energy argument in homogeneous Besov space framework to study the large time behavior of global‐in‐time strong solutions to the Cauchy problem of the three‐dimensional incompressible nematic liquid crystal flows with low regularity assumptions on initial data. More precisely, if the small initial data with 1 < p < ∞ and further assume that with 1 < q≤p and , then the global‐in‐time strong solution (u,d) to the nematic liquid crystal flows admits the following temporal decay rate: Here, is a constant unit vector. The highlight of our argument is to show that the ‐norms (with ) of solution are preserved along time evolution. Copyright © 2016 John Wiley & Sons, Ltd. |
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Keywords: | nematic liquid crystal flows energy argument Besov space temporal decay subclass 76A15 35B65 35Q35 |
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