Local Well-Posedness for Relaxational Fluid Vesicle Dynamics

TL;DR

This paper establishes the local well-posedness of a fluid vesicle dynamics model using a contraction mapping approach based on maximal regularity, providing a rigorous mathematical foundation for the model.

Contribution

It introduces a novel proof of local well-posedness for the relaxational fluid vesicle dynamics model via maximal Lp-regularity and contraction mapping techniques.

Findings

Proves local well-posedness of the model.

Uses maximal Lp-regularity of the linearized system.

Employs contraction mapping argument for the proof.

Abstract

We prove the local well-posedness of a basic model for relaxational fluid vesicle dynamics by a contraction mapping argument. Our approach is based on the maximal $L_p$-regularity of the model's linearization.