On decay estimates of the 3D nematic liquid crystal flows in critical Besov spaces

详细信息    查看全文

• 作者：Qiao Liu and Jihong Zhao
• 刊名：Mathematical Methods in the Applied Sciences
• 出版年：2016
• 出版时间：30 September 2016
• 年：2016
• 卷：39
• 期：14
• 页码：4044-4055
• 全文大小：268K
• ISSN：1099-1476

文摘

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 (u0,d0−d¯0)∈Ḃp,13p−1(R3)×Ḃp,13p(R3) with 1 < p < ∞ and further assume that (u0,d0−d¯0)∈Ḃq,∞−s(R3)×Ḃq,∞−s+1(R3) with 1 < q≤p and max0,1−3q≤s<min4−3q,1+3p, then the global-in-time strong solution (u,d) to the nematic liquid crystal flows admits the following temporal decay rate: