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October  2007, 8(3): 539-556. doi: 10.3934/dcdsb.2007.8.539

Analysis of a phase field Navier-Stokes vesicle-fluid interaction model

Qiang Du 1, , Manlin Li 1, and  Chun Liu 2,

1. 

Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States
2. 

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

Received  August 2006 Revised  February 2007 Published  July 2007

This paper is concerned with the dynamics of vesicle membranes in incompressible viscous fluids. Some rigorous theory are presented for the phase field Navier-Stokes model proposed in [7], which is based on an energetic variation approach and incorporates the effect of bending elasticity energy for the vesicle membranes. The existence and uniqueness results of the global weak solutions are established.
Keywords: Weak Solution, Phase Field, Bending Elastic Energy., Existence, Uniqueness, Navier-Stokes, Fluid Interaction, Vesicle Membrane, Well-posedness.
Mathematics Subject Classification: Primary: 58F1.
Citation: Qiang Du, Manlin Li, Chun Liu. Analysis of a phase field Navier-Stokes vesicle-fluid interaction model. Discrete and Continuous Dynamical Systems - B, 2007, 8 (3) : 539-556. doi: 10.3934/dcdsb.2007.8.539
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