On energetic variational approaches in modeling the nematic liquid crystal flows

Chun Liu; Huan Sun

doi:10.3934/dcds.2009.23.455

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2009, Volume 23, Issue 1&2: 455-475. Doi: 10.3934/dcds.2009.23.455

This issue Previous Article Non-linear electromagnetism and special relativity Next Article Quasilinear elliptic equations with signed measure

On energetic variational approaches in modeling the nematic liquid crystal flows

Chun Liu^1, and
Huan Sun^1,

1.
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

Received: January 31, 2008

Revised: March 31, 2008

Published: April 2009

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Abstract

In this paper we present results for the existence of classicalsolutions of a hydrodynamical system modeling the flow of nematicliquid crystals. The system consists of a coupled system ofNavier-Stokes equations and various kinematic transport equationsfor the molecular orientations. A formal physical derivation of theinduced elastic stress using least action principle reflects thespecial coupling between the transport and the induced stress terms.The derivation and the analysis of the system falls into a generalenergetic variational framework for complex fluids with elasticeffects due to the presence of nontrivial microstructures.

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Mathematics Subject Classification: Primary: 76D05, 35Q35; Secondary: 76D03, 76A05.

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