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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 classical solutions of a hydrodynamical system modeling the flow of nematic liquid crystals. The system consists of a coupled system of Navier-Stokes equations and various kinematic transport equations for the molecular orientations. A formal physical derivation of the induced elastic stress using least action principle reflects the special coupling between the transport and the induced stress terms. The derivation and the analysis of the system falls into a general energetic variational framework for complex fluids with elastic effects 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 - A, 2009, 23 (1&2) : 455-475. doi: 10.3934/dcds.2009.23.455
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