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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Gianni Dal Maso
Title: An existence and uniqueness result for the dynamics of micro-swimmers

Abstract: We present a model for the motion of micro-swimmers in a viscous fluid. Our 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 assume the self propulsion constraint (no external forces an momenta). Therefore, the 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 momentum, the equations of motion can be manipulated and turn out to be a system of six ordinary differential equations. Variational techniques are used to prove the continuity in time of its coefficients, so that the classical results on ordinary differential equations can be invoked to get the existence and uniqueness of the solution.

Date: Thursday, May 6, 2010
Time: 1:30 pm
Location: PPB 300