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

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Maso, Gianni Dal DeSimone, Antonio Morandotti, Marco
Copyright Year	2011
Abstract	We present an analytical framework to study the motion of microswimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of body shape uniquely determines 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 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 this system's coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.
Starting Page	1345
Ending Page	1368
Page Count	24
File Format	PDF
ISSN	00361410
DOI	10.1137/10080083X
e-ISSN	10957154
Journal	SIAM Journal on Mathematical Analysis (SJMAAH)
Issue Number	3
Volume Number	43
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-06-07
Access Restriction	Subscribed
Subject Keyword	Biopropulsion in water and in air swimming Fluid-solid interactions Second-order elliptic systems low Reynolds number flows dependence of solutions of PDEs on domain and boundary data Existence, uniqueness, and regularity theory Stokes equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis Computational Mathematics

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