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.

引用

页码：979 / 992

页数：14

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