On a Stokes-type system arising in fluid vesicle dynamics

Daniel Lengeler

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arXiv · 1506.08991

On a Stokes-type system arising in fluid vesicle dynamics

Daniel Lengeler

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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.

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Daniel Lengeler. 2015-06-30. On a Stokes-type system arising in fluid vesicle dynamics. https://arxiv.org/abs/1506.08991

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