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November  2003, 3(4): 481-494. doi: 10.3934/dcdsb.2003.3.481

Regularity properties of planar motions of incompressible rods

Stuart S. Antman 1,

1. 

Department of Mathematics,Institute for Physical Science and Technology, and Institute for Systems Research, University of Maryland, College Park, MD 20742, United States

Received  October 2002 Revised  March 2003 Published  August 2003

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.
Keywords: Incompressible rods, a priori bounds..
Mathematics Subject Classification: 74K10, 74B20, 35B3.
Citation: Stuart S. Antman. Regularity properties of planar motions of incompressible rods. Discrete & Continuous Dynamical Systems - B, 2003, 3 (4) : 481-494. doi: 10.3934/dcdsb.2003.3.481
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