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

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

Pages: 539 - 556, Volume 8, Issue 3, October 2007

doi:10.3934/dcdsb.2007.8.539       Abstract        Full Text (207.8K)       Related Articles

Qiang Du - Department of Mathematics, Pennsylvania State University, University Park, PA 16802, United States (email)
Manlin Li - Department of Mathematics, 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: 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:  Phase Field, Navier-Stokes, Well-posedness, Weak Solution, Existence, Uniqueness, Vesicle Membrane, Fluid Interaction, Bending Elastic Energy.
Mathematics Subject Classification:  Primary: 58F15.

Received: August 2006;      Revised: February 2007;      Published: July 2007.