Nonrelativistic and Relativistic Continuum Mechanics

TL;DR

This paper develops a unified spacetime framework for both nonrelativistic and relativistic elasticity, focusing on causality and local existence theorems for the initial-value problem.

Contribution

It introduces a comprehensive spacetime formulation for elasticity theories, emphasizing causal structure and local existence results, building on joint work by Schmidt and the author.

Findings

Unified spacetime formulation for elasticity theories

Analysis of causal structures in nonrelativistic and relativistic contexts

Establishment of local existence theorems for initial-value problems

Abstract

There is described a spacetime formulation of both nonrelativistic and relativistic elasticity. Specific attention is devoted to the causal structure of the theories and the availability of local existence theorems for the initial-value problem. Much of the presented material is based on joint work of B.G.Schmidt and the author (in Class.Quantum Grav.\textbf{20} (2003), 889-904).