Regularity Properties of Planar Motions of Incompressible Rods

This paper treats the quasilinear evolution equations governing the planar motions of incompressible rods. Since incompressibility is here a 2dimensional 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.