On the motion of a compact elastic body

TL;DR

This paper investigates the dynamics of a relativistic elastic solid with free boundaries, proving short-term existence and uniqueness of solutions near a stress-free, rigid motion state using advanced mathematical techniques.

Contribution

It introduces a novel application of Koch's theorem to establish short-time well-posedness for relativistic elastic bodies in a Lagrangian framework.

Findings

Proved short-time existence and uniqueness of solutions

Established stability near stress-free rigid motion

Applied mathematical techniques to relativistic elasticity

Abstract

We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations in material form ("Lagrangian coordinates"). By applying a basic theorem due to Koch, we prove short-time existence and uniqueness for solutions close to a trivial solution. This trivial, or natural, solution corresponds to a stress-free body in rigid motion.