Communications in Mathematical Sciences

Volume 11 (2013)

Number 3

Long-time dynamics of the nonhomogeneous incompressible flow of nematic liquid crystals

Pages: 779 – 806

DOI: https://dx.doi.org/10.4310/CMS.2013.v11.n3.a6

Authors

Xianpeng Hu (Courant Institute of Mathematical Sciences, New York University, New York, N.Y., U.S.A.)

Hao Wu (School of Mathematical Sciences and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shangha, China)

Abstract

We study the long-time behavior of global strong solutions to a hydrodynamic system for nonhomogeneous incompressible nematic liquid crystal flows driven by two types of external forces in a smooth bounded domain of dimension two. For arbitrary large regular initial data with the initial density being away from vacuum, we prove the decay of the velocity field for both cases. Furthermore, for the case with asymptotically autonomous external force, we can prove the convergence of the density function and the director vector as time goes to infinity. Estimates on the convergence rate are also provided.

Keywords

nonhomogeneous nematic liquid crystal flow, long-time behavior, uniqueness of asymptotic limit, convergence rate

2010 Mathematics Subject Classification

35B40, 35B41, 35Q35, 76D05

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Published 14 May 2013