MENU

You are here

An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers

TitleAn Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers
Publication TypeJournal Article
Year of Publication2011
AuthorsDal Maso, G, DeSimone, A, Morandotti, M
JournalSIAM J. Math. Anal. 43 (2011) 1345-1368
Abstract

We present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

URLhttp://hdl.handle.net/1963/3894
DOI10.1137/10080083X

Sign in