کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6417220 | 1338551 | 2015 | 30 صفحه PDF | دانلود رایگان |

In recent paper [7], Y. Du and K. Wang (2013) proved that the global-in-time Koch-Tataru type solution (u,d) to the n-dimensional incompressible nematic liquid crystal flow with small initial data (u0,d0) in BMOâ1ÃBMO has arbitrary space-time derivative estimates in the so-called Koch-Tataru space norms. The purpose of this paper is to show that the Koch-Tataru type solution satisfies the decay estimates for any space-time derivative involving some borderline Besov space norms. More precisely, for the global-in-time Koch-Tataru type solution (u,d) to the nematic liquid crystal flow with initial data (u0,d0)âBMOâ1ÃBMO and âu0âBMOâ1+[d0]BMOâ¤Îµ for some small enough ε>0, and for any positive integers k and m, one hasâtk+m2(âtkâmu,âtkâmâd)âLËâ(R+,BËâ,ââ1)â©LË1(R+;BËâ,â1)â¤Îµ. Furthermore, we shall give that the solution admits a unique trajectory which is Hölder continuous with respect to space variables.
Journal: Journal of Differential Equations - Volume 258, Issue 12, 15 June 2015, Pages 4368-4397