Finite-dimensional global attractor for a system modeling the 2D nematic liquid crystal flow

被引：22
作者：
Grasselli, M. [1 ]
Wu, H. [2 ]
机构：
[1] Politecn Milan, Dipartimento Matemat F Brioschi, I-20133 Milan, Italy
[2] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Sch Math Sci, Shanghai 200433, Peoples R China
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2011年 / 62卷 / 06期
关键词：
Liquid crystal flow; Kinematic transport; Global attractor; Finite fractal dimension; APPROXIMATION; REGULARITY; EXISTENCE;
D O I：
10.1007/s00033-011-0157-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a 2D system that models the nematic liquid crystal flow through the Navier-Stokes equations suitably coupled with a transport-reaction-diffusion equation for the averaged molecular orientations. This system has been proposed as a reasonable approximation of the well-known Ericksen-Leslie system. Taking advantage of previous well-posedness results and proving suitable dissipative estimates, here we show that the system endowed with periodic boundary conditions is a dissipative dynamical system with a smooth global attractor of finite fractal dimension.
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页码：979 / 992
页数：14
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