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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

On energetic variational approaches in modeling the nematic liquid crystal flows

Pages: 455 - 475, Volume 23, Issue 1/2, January/February 2009

doi:10.3934/dcds.2009.23.455       Abstract        Full Text (237.6K)       Related Articles

Huan Sun - Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States (email)
Chun Liu - Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States (email)

Abstract: 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, Existence, Non-newtonian fluids
Mathematics Subject Classification:  Primary: 76D05, 35Q35; Secondary: 76D03, 76A05

Received: February 2008;      Revised: April 2008;      Published: September 2008.