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January & February  2009, 23(1&2): 455-475. doi: 10.3934/dcds.2009.23.455

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, United States

Received  February 2008 Revised  April 2008 Published  September 2008

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.
Keywords: Navier-Stokes Equations, Non-newtonian fluids, Existence.
Mathematics Subject Classification: Primary: 76D05, 35Q35; Secondary: 76D03, 76A05.
Citation: Chun Liu, Huan Sun. On energetic variational approaches in modeling the nematic liquid crystal flows. Discrete & Continuous Dynamical Systems, 2009, 23 (1&2) : 455-475. doi: 10.3934/dcds.2009.23.455
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