On a Stokes-type system arising in fluid vesicle dynamics

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 $L_2$-analysis of the Stokes-type system that takes into account geometric variations of the fluid vesicle.

51 pages; eliminated some typos and gave a more precise proof of Lemma 3.9; changed a few lines in the introduction

References in corpus (2)

• Numerical computations of the dynamics of fluidic membranes and vesicles
• An elementary proof of the continuity from $L_0^2(\Omega )$ to $H_0^1(\Omega {)}^n$ of Bogovskii's right inverse of the divergence

Cited by in corpus (2)

• Incompressible fluid problems on embedded surfaces: Modeling and variational formulations
• Parametric finite element approximations of curvature driven interface evolutions