On a Stokes-type system arising in fluid vesicle dynamics

2015/06/30 by Daniel Lengeler, Lengeler, Daniel
Biochemistry, Genetics and Molecular Biology · Medicine · #Lipid Membrane Structure and Behavior #Erythrocyte Function and Pathophysiology #Blood properties and coagulation

paper · pdf · doi:10.48550/arxiv.1506.08991

Abstract

This article is the first in a series of papers on the analysis of a basic model for fluid vesicle dynamics. There are two variants of this model, a parabolic one decribing purely relaxational dynamics and a non-parabolic one containing the full dynamics. At the heart of both variants lies a linear elliptic system of Stokes-type. Understanding the mapping properties of this Stokes-type system is crucial for all further analysis. In this article we give a basic exposition of the dynamical model and a thorough L₂-analysis of the Stokes-type system that takes into account geometric variations of the fluid vesicle.

Citations

• Configurations of fluid membranes and vesicles
• An elementary proof of the continuity from L₀²(Ω) to H¹₀(Ω)ⁿ of Bogovskii's right inverse of the divergence

Related

• Shape dynamics of nearly spherical, multicomponent vesicles under shear flow
• Nearly spherical vesicles in an external flow
• Onsager's Variational Principle for the Dynamics of a Vesicle in a Poiseuille Flow
• Non-equilibrium dynamics of initially spherical vesicles in general flow
• Dynamics of a multicomponent vesicle in shear flow