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

Qiang Du; Manlin Li; Chun Liu

doi:10.3934/dcdsb.2007.8.539

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2007, Volume 8, Issue 3: 539-556. Doi: 10.3934/dcdsb.2007.8.539

This issue Previous Article Analytical solutions for phase transitions in a slender elastic cylinder under non-deforming and other boundary conditions Next Article Numerical methods for stiff reaction-diffusion systems

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

1.
Department of Mathematics, Pennsylvania State University, University Park, PA 16802
2.
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802

Received: July 31, 2006

Revised: January 31, 2007

Published: April 2007

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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.

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Mathematics Subject Classification: Primary: 58F15.

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