Department of Mathematics,Institute for Physical Science and Technology, and Institute for Systems Research, University of Maryland, College Park, MD 20742
This paper treats the quasilinear evolution equations governing the planar motions of incompressible
rods. Since incompressibility is here a 2-dimensional phenomenon, a thickness variable
enters the governing equations in an essential and novel way. These equations have a mathematical structure
strikingly different from that for compressible rods.
In contrast to the case for compressible rods, the governing equations admit
a priori upper and lower bounds on the stretches without the
viscosity becoming singular when these stretches
reach their extremes.