Wellposedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation

TL;DR

This paper establishes the well-posedness of a 3-D fluid-structure interaction model describing a self-propelled swimmer in an incompressible fluid governed by the nonstationary Stokes equation, extending previous 2-D models.

Contribution

It extends the 2-D swimming model to 3-D, providing mathematical analysis of existence and uniqueness of solutions for this more complex setting.

Findings

Proved well-posedness of the 3-D swimmer model

Extended the mathematical framework from 2-D to 3-D

Applicable to biological and engineering propulsion systems

Abstract

We introduce and investigate the wellposedness of a model describing the self-propelled motion of a small abstract swimmer in the 3-D incompressible fluid governed by the nonstationary Stokes equation, typically associated with the low Reynolds numbers. It is assumed that the swimmer's body consists of finitely many subsequently connected parts, identified with the fluid they occupy, linked by rotational and elastic Hooke's forces. In this paper we are attempting to extend the 2-D version of this model, introduced in [18]-[20], to the 3-D case. Models like this are of interest in biological and engineering applications dealing with the study and design of propulsion systems in fluids.