Department of Mathematics Colloquium


Abstract 

The swimming phenomenon has been a
source of great interest and inspiration for many researchers for
a long time, with formal publications traced as far back as to the
works of G. Borelli in 16801681. The goal of this particular
lecture is to discuss how the geometric shape of a swimmer affects the
forces acting upon it in a 3D incompressible fluid, such as governed
by the nonstationary Stokes or NavierStokes equations. Namely,
we are interested in the following question: How will the
swimmer's internal forces (i.e., not moving the center of swimmer's
mass when it is not inside a fluid) ``transform'' their actions when
the swimmer is placed inside a fluid (thus, possibly,
creating its selfpropelling motion)? We focus on the case
when the swimmer's body consists of either small parallelepipeds
or balls. Such problems are of interest in biology and engineering
application, as well as in mathematical control theory, dealing
with propulsion systems in fluids. This is a joint work with Giangbang Trinh.
